A compressed sensing (CS) based channel estima-tion algorithm is proposed by using the delay-Doppler sparsity of the fast fading channel. A compressive basis expansion chan-nel model with sparsity in both time and frequency domains is given. The pilots in accordance with a novel random pilot ma-trix in both time and frequency domains are sent to measure the delay-Doppler sparsity channel. The relatively nonzero channel coefficients are tracked by random pilots at a sampling rate signifi-cantly below the Nyquist rate. The sparsity channels are estimated from a very limited number of channel measurements by the basis pursuit algorithm. The proposed algorithm can effectively improve the channel estimation performance when the number of pilot sym-bols is reduced with improvement of throughput efficiency.