Abstract: Based on Kalman filter (KF) and compressive sensing (CS) theory，we proposed a modified KF compressive sensing (MKFCS) algorithm which aims at reconstructing time sequences of spatially sparse signals with unknown and time varying sparsity supports. First, the residual of the signal, which could indicate the position of the new supports, is estimated using KF. Then a new supports is decided by means of a modified CS algorithm. Finally, the signal with unknown and time varying sparsity support is reconstructed using least square via the updated supports adaptively. And the MKFCS algorithm is performed through simulating reconstruction accuracy, reconstruction error and its stability to validate the algorithm. Simulation results and theoretical anylasis show that the proposed method has many advantages such as needing fewer measurements than existing methods, having higher reconstruct accuracy and better robust etc..