The changes of temperature and strain will cause the center wavelength drift of fiber Bragg grating (FBG) reflection wave. The FBG can be combined with giant magnetostrictive material (GMM) to measure the current, but the cross sensitivity of temperature and strain seriously affects the accuracy of the current measurement. The neural network has strong nonlinear mapping ability, which can adaptively find out the internal law of the sensor to compensate the temperature effectively. For the problem of neural network is easy to fall into the local minimum, the genetic algorithm is applied to optimize weights and thresholds of neural network and find the optimal solution of weights and thresholds quickly and accurately. In order to improve the reliability of the network prediction, the K fold cross validation method is used to solve the problem of small sample size. The experimental results show that the mean square error of the optimized neural network for current prediction is 0.0038, which improves the measurement accuracy of FBG current sensor.