Inverse problems arise in scientific and technical fields such as geophysics, life science, remote sensing technology, pattern recognition, financial science, etc. Therefore, inverse problems have attracted much attention and have been studied by many authors. However it is usually difficult to solve inverse problems. In particular, most inverse problems are very complex with a large amount of calculation. Thus, it is very important to obtain the algorithm to solve inverse problems with advantages such as high precision, little calculation, good convergence and strong stability. Good properties of reproducing kernel in calculation made it an important function approximation technique. In recent years, reproducing kernel theory is developing very rapidly, and successfully applied to wavelet transforms, signal processing, stochastic processes, iris recognition, neural network, and so on.