The bond purchases have kept long-term interest rates low, encouraging more borrowing and spending.
Evans said the purchases could be slowed stages and that the program could end by the middle of next year, if unemployment falls to around 7 percent. His remarks were in line with previous comments made by Fed Chairman Ben Bernanke.
The unemployment rate fell in July to 7.4 percent, down from 7.6 percent in June. The economy has been adding jobs at a steady but inconsistent pace this year. In July, employers added 162,000 jobs. While solid, that's much slower than the average pace of 192,000 new jobs a month added so far this year. And many of the jobs added last month were low-paying or part-time.
The economy grew at a sluggish annual rate of 1.4 percent in the first half of the year. But Evans forecasts that overall economic growth could accelerate to an annual rate of around 2.5 percent in the second half of this year.
And stronger trade report released Tuesday has private economists predicting that growth in the April-June quarter could be revised up sharply from the 1.7 percent annual pace reported last week.
Even if the bond program ends next year, Evans said the Fed will likely have purchased at least $1.2 trillion in mortgage and Treasury bonds since September 2012. Evans said the program has been "quite successful," countering critics who charge that it has done little to boost economic growth.