We deduced the stellar beta-decay rate of Fe-59 at typical carbon-shell burning temperature by taking the experimental Gamow-Teller transition strengths of the Fe-59 excited states. The result is also compared with those derived from large-scale shell model calculations. The new rate is up to a factor of 2.5 lower than the theoretical rate of Fuller, Fowler, and Newman (FFN) and up to a factor of 5 higher than decay rate of Langanke and Martinez-Pinedo (LMP) in the temperature region 0.5 <= T <= 2 GK. We estimated the impact of the newly determined rate on the synthesis of cosmic gamma emitter Fe-60 in C-shell burning and explosive C/Ne burning using a one-zone model calculation. Our results show that Fe-59 stellar beta decay plays an important role in Fe-60 nucleosynthesis, even though the uncertainty of the decay rate is rather large due to the error of B(GT) strengths.