Infrared point target detection is one of the key technologies of the infrared guidance system. On the one hand, due to the long observation distance, the point target is often submerged in the background clutter and large noise in the process of atmospheric transmission and scattering, and the signal-to-noise ratio is low. On the other hand, the target in the image appears in the form of fuzzy points, so that the target has no obvious features and texture information. Therefore, due to these two factors, infrared point target detection becomes intensely difficult. In order to address the issue, the relevant algorithms of point infrared target detection are studied, and a combination algorithm of non-convex rank approximation minimization algorithm and the modified random walker algorithm (NRAM-MRW) is proposed, which has a better detection effect of point infrared target detection under complex background.