A superconvergent finite point method (SFPM) is proposed and analyzed for solving linear biharmonic problems. Firstly, the smoothed derivative is introduced into the moving least squares approximation, and a superconvergent finite point method based on the smoothed gradient is constructed to obtain high accuracy and superconvergent numerical results. Secondly, the theoretical accuracy of the SFPM is provided through local truncation error analysis. Finally, the superconvergence of the method and the correctness of the theoretical analysis are verified through numerical experiments.