Abstract: High data rates and high mobility introduce time and frequency selectivity in wideband wireless communication. We need to estimate the channel state information so that the data through fading channel can be received correctly. Exploiting the sparsity of doubly selective wireless channel in both delay domain and Doppler domain, we study the doubly selective channel estimation based on compressed sensing. In order to overcome the instability of the channel estimation caused by the multipath delay spread and Doppler shift, the channel estimation based on ROMP algorithm is studied in this paper. Theoretical analysis and simulation show that the compressive sensing estimation has better performance but with fewer pilots than conventional least square estimation, furthermore, ROMP has better estimation performance than OMP with higher robustness.