* Hamburg's down-to-earth mayor seen as new finance minister
* Former labour minister has no big experience on EU level
* Works well with Merkel, but also critical of her style
* Could shape euro zone reform debate in tandem with Schulz
BERLIN, Feb 7 (Reuters) - Olaf Scholz, the mild-mannered, pragmatic mayor of Hamburg who could become Germany's next finance minister, had a baptism of fire last summer during violent riots surrounding the G20 summit in his city.
Scholz apologised publicly for the security fiasco, but stayed calm in the face of furious attacks by right-wing critics, who accused him of being too soft on anti-capitalist violence.
The 59-year old Social Democrat, a trained lawyer and strong advocate of closer European integration, later said the extent of the violence had rattled him and that he would have resigned if anyone had been killed.
That quiet resolve could serve Scholz well as he steps into the giant shoes left by Wolfgang Schaeuble, the fiscally hawkish and larger-than-life veteran of German politics who now presides over the lower house of parliament, the Bundestag.
Some conservatives fear Scholz, who recently backed a big increase in the minimum wage, could raise government spending and reverse's Schaeuble "black zero" policy of not incurring new debt.
Others say that Scholz is likely to stick to Germany's fiscal conservatism but may adopt a more conciliatory tone towards poorer euro zone countries such as Greece.
Business executives could also have trouble convincing Scholz to adopt new corporate tax cuts modelled on those passed in the United States, which have triggered a flood of investment.
"We have made our corporate tax structure competitive internationally in recent years. There is no need for hectic corrections," he told the business magazine Wirtschaftswoche.
Scholz also backs higher tax rates for the wealthy, although he often tells audiences: "I can only distribute what I've earned."
Scholz has long been more popular among SPD members than party leader Martin Schulz. In 2011, he led the SPD out of opposition to win an majority in Hamburg's state election. Four years later, SPD support had shrunk, but he was able to pull together a ruling coalition with the environmentalist Greens.
He works well with Chancellor Angela Merkel, a fact that was evident during a series of joint appearances during the Hamburg G20 summit, and dates back to his tenure as labour minister during Merkel's first "grand coalition" from 2005 to 2009.
"EU MUST DEVELOP"
Scholz, an attorney, has little experience on the EU stage, but would work together closely with Schulz - former president of the European Parliament and likely foreign minister in Merkel's next government - on issues such as euro zone reform.
In December, Scholz told the newspaper Die Welt that Germany urgently needed to respond to proposals by French President Emmanuel Macron.
"The EU is not just a customs union. It must develop joint policies in the area of foreign and security, migration, finance, economy," he said.
"And these policies must be different from those of the chancellor, who leaves many things unspoken and works out deals behind closed doors in Brussels in the middle of the night," he added. "We have to state clearly what we are planning on the European policy front. We need to be more bold."
One key concern for Scholz has been digitalisation and how Western democracies should respond to the rise of right-wing populism and growing doubts about the benefits of globalisation, particularly given a stagnation in wages at the same time as Germany lacks skilled workers.
Scholz's wife, Britta Ernst, is education minister in the eastern state of Brandenburg, surrounding Berlin.
He himself is sporty, showing up for coalition talks at least once in a jogging suit.
Like Schaeuble, he has an occasional sharp tongue.
Last week, he brushed aside a question about his ambition to take over as finance minister, brusquely telling a reporter: "What is that question supposed to mean?"
In December, he grew irritated by repeated questions from Die Welt about his failure to challenge Schulz for the party's leadership after it eked out the worst election result since Germany became a federal republic in 1949.
"I don't like the tendency to let personnel issues overshadow important issues of substance," he told the paper. "The SPD suffered a serious loss and we have to analyse clearly what went wrong. At the same time, we have to discuss how we can live up to our responsibility for the country. The game of who loves whom doesn't help us there." (Additonal reporting by Michael Nienaber; Editing by Kevin Liffey)