Abstract: To address the model uncertainty problem of the synthesis approach of the predictive control, a new synthesis method of adaptive predictive control based on recursive subspace which is different from the previous methods with polytopic description is proposed. Hankel matrix is rebuilt by adding the current input and output data in each step, and then the extended observability matrix is updated. The corresponding state space model is obtained and then is used in current control of optimization solution to get the current control law. To improve the convergence rate of the algorithm, a model matching error based time-varying forgetting factor is introduced into the identification process. Finally, two simulation examples are presented in the linear time-invariant and the slow time varying situations, and the results verify the effectiveness of the proposed algorithm.