As a next generation FEL light source based on linac, high repetition rate operation to increase average FEL power has been proposed, e.g. LCLS-II project. The injector, which generates high brightness and high average current beam, is one of key components. A photocathode DC gun and superconducting RF cavities, which are developed for ERL light source, can be employed for the high repetition rate injector. For high repetition rate operation of FEL light source, injector simulations were carried out based on ERL injector with demonstrated hardware performance by the cERL beam operation in KEK. The optimization results show that the gun voltage of 500 kV is helpful to achieve low emittance. In addition, to estimate optimum gun voltage and cavity acceleration gradient for the FEL operation, two optimizations with different injector layouts were carried out. The results show that the both different layouts have potential to achieve target emittance for FEL operation. Under the realistic operation condition, the transverse normalized rms emittance of 0.8 mm mrad with the rms bunch length of 3 ps, the bunch charge of 325 pC, and the beam energy of 10 MeV is obtained from the optimizations.