Abstract: A new model-free learning control algorithm for nonlinear motion control based on Fourier infinite series mapping is presented. With this algoirithm, the complex nonlinear problem can be changed into that of several regulators in Fourier space, thus this algorithm will be simple and easy to realize. The detailed description and proof of this control algorithm is derived. Finally, the experimental result is given, and shows that it can be regarded as a good control algorithm for precision tracking.