An adaptive projection iterative algorithm for solving a class of free boundary problems with bilateral obstacles was developed. The finite difference method was used to discretize the obstacle problem into a finite dimensional two-sided obstacle problem, which was equivalent to a new projection fixed point problem, and the projection algorithm for the two-sided obstacle problem was obtained. The parameters are automatically adjusted by iterating data to accelerate convergence. An adaptive projection algorithm for solving bilateral obstacle problem was proposed, and the algorithm process and convergence analysis were given. Both theoretical analysis and numerical examples demonstrate the effectiveness of the proposed algorithm.