Inflation has been running persistently below the 2 percent target the central bank likes to see as indicative of healthy economic growth. Some officials have expressed caution about the Fed's collective desire to keep raising rates in that climate.
However, George said she feels confident enough in where things stand to keep advocating for tighter policy.
"I think we should continue with the gradual rate path," she told CNBC in a live interview from the annual symposium in Jackson Hole, Wyoming, that the Kansas City Fed hosts. "While we haven't hit 2 percent, I'm reminded that 2 percent is a target over the long term, and in the context of a growing economy, of jobs being added, I don't think it's an issue that we should be particularly concerned about unless we see something change."
The Fed began hiking rates in December 2015 after slashing its benchmark funds rate to near-zero during the financial crisis and keeping it there for seven years. Since that increase, the Fed has hiked three more times, with the current target now 1 to 1.25 percent.
Inflation, though, has presented a quandary. The core Consumer Price Index, which measures a basket of goods excluding food and energy, rose 1.7 percent annualized in July. The Fed's preferred measure, the personal consumption expenditures index, most recently showed a 1.5 percent gain.
However, George said she was not bothered by the low readings.
"Inflation is running close enough to 2 percent in my view that it allows a gradual approach," she said.
George has been one of the more hawkish Fed members, occasionally voting against her colleagues when it comes to determining the path of rates. Traders in the funds market do not expect the Fed to approve more hikes this year, even though officials continue to insist that another move is in play.
For her part, George has been a believer that the economy is strong enough to handle rate hikes, though her current forecast remains for just a 2 percent GDP gain this year.
"I'm delighted that the unemployment rate is low and more people have jobs," she said. "But I do look carefully at how you ensure that you have sustained growth in the long run, and an overheating labor market can be an issue for you in the long term."
The current unemployment rate is 4.3 percent, the lowest in 16 years.