According to a class of free boundary problems, a selfadaptive projection algorithm based on linear complementarity problem is put forward, The free boundary problem is discretized by the finite difference method and formulated as a linear complementarity problem, then the selfadaptive projection iteration algorithm is used to obtain its numerical solution, this method automatically adjusts parameters in iterative process to attain the goal of accelerating the convergence speed, and this method only needs to solve a system of linear equations for each iteration. The detailed algorithm process is given, their convergence analysis is obtained by projection properties. Finally, the numerical examples are used to test the algorithm, compared with the existed algorithms, this method has more rapid convergence speed because the parameter has little effect on the selfadaptive projection algorithm.