We present a gain adaptive tuning method for fiber Raman amplifier (FRA) using two-stage neural networks (NNs) and double weights updates. After training the connection weights of two-stage NNs separately in training phase, the connection weights of the unified NN are updated again in verification phase according to error between the predicted and target gains to eliminate the inherent error of the NNs. The simulation results show that the mean of root mean square error (RMSE) and maximum error of gains are 0.131 dB and 0.281 dB, respectively. It shows that the method can realize adaptive adjustment function of FRA gain with high accuracy.