The neutron capture cross section of long-lived radioactive 205Pb is derived by using the nuclear reaction calculation code CCONE, based on photonuclear data. The present result is smaller than that of TENDL-2015 by a factor of 4. The derived Maxwellian averaged capture cross section (MACS) is the smallest compared to the existing data. The produced amount of 205Pb is explored with a simulated neutron flux in the Pb-Bi eutectic (LBE) target. The continuous use of the system in 25 years creates 205Pb with about 6 kg at maximum in the LBE (including natural Pb of 103 kg). The impact of the derived MACS on the stellar nucleosynthesis is investigated. It is found that the abundance of Tl is slightly enhanced due to the increase in the remaining abundance of 205Pb.