The invention provides an image super-resolution reconstruction method for an FPM algorithm based on nonlinear optimization. The method includes following steps: (1) LEDs in an LED array are controlled to emit light point by point, and an FPM platform acquires low-resolution images in different illuminations; (2) the obtained images based on different angle illuminations are actually characteristics obtained by shifting of images in a frequency domain in the normal incidence, restraint of the acquired low-resolution images is set up, and the total deviation between a reconstruction result and the acquired images is defined based on the constraint; and (3) a corresponding gradient value is obtained via derivation of the total deviation, and the reconstruction result with minimum total deviation is obtained via iterative solution by employing a gradient descent algorithm. According to the method, advantages of the nonlinear optimization method are fully used, mathematical modeling of the original FPM algorithm is performed, the method of frequency domain iteration is abstracted to a problem of solving a non-linear function and obtaining an optimal solution, the problem of image super-resolution reconstruction is solved from a new angle, and the reconstruction effect of the algorithm is improved.