Magnetic resonance imaging (MRI) suffers the geometrical distortion caused by gradient non-linearity, which is because of the imperfection of the hardware, such as gradient coil. The traditional correction method employs spherical harmonic function to calculate position of each voxel. However, the spherical harmonic function is constructed based on gradient coil design information, such as magnetic field distribution, which is hard to obtain for users and some venders who use commercial coils. Since the gradient field distribution is not provided by our coil supplier, this paper applied BP (back propagation) neural network to correct image distortions. Compared with traditional technique, the method proposed in this paper is able to correct distortions simply without using gradient coil information. The method calculated the real and practical position of landmark points that are selected as train dataset based on phantom structure. After training, the full image pixel coordinates could be calculated by trained neural network model. Interpolation was used to calculate the image intensity after position correction. Great improvement has been observed in each direction after correction. The correction method can be practically useful.