Structure Illumination Microscopy (SIM) is a wide-field super-resolution fluorescence imaging technology with characteristics such as fast imaging speed and low phototoxicity. By projecting sinusoidal patterns at the sample plane, the high-frequency information in Fourier space which is out of the optical transfer function of the optical system is loaded into the low-frequency information and collected by the objective lens. However, due to the mechanical error of the system, the fringes in the collected data often have some deviation from the presupposed initial values. These systemic errors of fringe will directly affect the quality of the reconstructed SIM image, among which Fringe modulation depth is a very important parameter. Here, we explored the SIM reconstruction method based on the U-net neural network architecture recently reported by Luhong Jin et al.We performed a simulation to validate the method. Specifically, we use an open source fluorescent-bead images for the training and testing. We found that after training, the output of the trained neural network is very close to the ground truth, and then the super-resolution information can be well recovered from the low-modulation SIM raw images. We then further performed the similar study on the images of real biological structures which are also available as an open source dataset. Our study thus demonstrates that the deep learning neural network algorithm can significantly relax the requirement on the fringe modulation depth.Therefore, the simplified SIM system without any polarization modulation can be expected.