Multipath channels often exhibit sparse structures in the multiple-input single-output orthogonal frequency division multiplexing (MISO-OFDM) systems. Conventional linear channel estimation methods, such as least squares (LS), are based on the implicit assumption of rich multipath which results in low spectral efficiency. In this paper, exploiting the channel sparsity, we propose a novel sparse channel estimation method based on compressive sensing and employ the adaptive compressive matching pursuit (ACMP) algorithm to recover the channel impulse response. Simulation results verify that the proposed compressive channel estimation method integrates the advantages of the existing ones and provides the excellent estimation performance and high bandwidth efficiency.