After investigating the structural features of burst signal, an improved sparse channel estimation algorithm is proposed based on compressive sensing. In the initial estimation, the autocorrelation property of preamble pseudo-random sequence is utilized to estimate the path delay of channel. Then the sparse recovery with the delay is initialized, which takes advantage of the prior information of channel estimation. In the follow-up channel estimation, the algorithm tracks the current channel information through the channel information estimated in the previous moment. Simulations indicate that the proposed algorithm improves channel estimation precision, and decreases the bit error rate of receiver system, when compared with the lease square estimation algorithm, orthogonal matching pursuit algorithm and sparse reconstruction by separable approximation algorithm.