Channel estimation of an orthogonal frequency division multiplexing (OFDM) system based on compressed sensing can effectively reduce the pilot overhead and improve the utilization rate of spectrum resources. The traditional SAMP algorithm with a fixed step size for sparse channel estimation has the disadvantages of a low estimation efficiency and limited estimation accuracy. An Improved SAMP (ImpSAMP) algorithm is proposed to estimate the channel state information of the OFDM system. In the proposed ImpSAMP algorithm, the received signal is firstly denoised based on the energy-detection method, which can reduce the interferences on channel estimation. Furthermore, the step size is adjusted dynamically according to the l₂ norm of difference between two estimated sparse channel coefficients of adjacent phases to estimate the sparse channel coefficients quickly and accurately. In addition, the double threshold judgment is adopted to enhance the estimation efficiency. The simulation results show that the ImpSAMP algorithm outperforms the traditional SAMP algorithm in estimation efficiency and accuracy.