Structured Illumination Microscopy (SIM) has been widely used in super-resolution imaging owing to its low phototoxicity and wide-field imaging capability. However, traditional SIM requires three phase-shifted images for each illumination direction and relies on accurate phase-shift estimation. Meanwhile, for samples with a certain thickness, reconstruction artifacts are easily introduced and image contrast is reduced due to out-of-focus effects. To address these issues, this paper proposes a physics-informed wavelet neural network (PIWNN) for super-resolution reconstruction based on crossed structured illumination. Crossed structured illumination enables high-frequency information from two directions to be simultaneously encoded into Moiré fringes, thereby improving data acquisition speed while effectively suppressing the influence of the zero-order spectrum under different illumination conditions on the reconstruction results. PIWNN combines the SIM physical model with wavelet network. The physical model is used to constrain reconstruction process and enhance high-frequency information of sample, while wavelet transform is employed to replace pooling operation for upsampling and downsampling, thereby information loss can be reduced and the receptive field can be enlarged. The proposed method can complete crossed-illumination SIM reconstruction using only five raw images with random phase shifts, without prior system parameters and pretraining datasets, imaging speed and reconstruction robustness can be improved significantly. Simulation and experimental results demonstrate that the proposed method effectively improves resolution and maintains high structural similarity and signal-to-noise ratio under low-illumination and noisy conditions.