Functional near-infrared spectroscopy (fNIRS) has attracted considerable attention in recent years in brain neuroscience as a brain imaging system with high temporal resolution, low cost, and high portability. However, motion artifacts in fNIRS signals interfere with the results of subsequent data analysis, and the denoising effect of some existing algorithms is insufficient. Therefore, a motion artifact correction algorithm for fNIRS signals based on a multilayer convolutional self-coding (MCAN) algorithm is proposed. The algorithm was used to correct three motion artifacts in the fNIRS signals. Next, the performance of the proposed algorithm was verified using simulation and experimental data and compared with several widely used algorithms. The results show that the MCAN algorithm performs satisfactorily in the remaining number of motion pseudo-traces, mean squared error, signal-to-noise ratio, square of Pearson correlation coefficient, and peak-to-peak error. Therefore, the proposed algorithm can be used as an efficient fNIRS signal preprocessing algorithm.