In the air ground frequency selective fading channel, the channel impulse response has the time domain sparse characteristic.In the light of the discovery mentioned above, the greedy algorithm based sparse channel estimation method for Single Carrier Frequency Domain Equalization (SC FDE) system is proposed in this paper.Chu sequence, the pilot sequence commonly used in SC FDE is analyzed, and it is proven that the pilot matrix constructed by the cyclic shift of Chu sequence has satisfied RIP condition.Thus, the pilot matrix is used as a measurement matrix, the air ground channel estimation issue is modeled as a sparse reconstruction model, and sparse reconstruction of the channel is performed with OPM and CoSaMP algorithms of the greedy algorithm.It is verified by simulation that:compared with the traditional Least Squares (LS) channel estimation method, the obtained channel estimation is of higher accuracy.With the same training sequence length and channel environment, the Minimum Mean Square Error (MMSE) equalization of received signal is performed by using the obtained channel estimation.The Monte Carlo simulation results show that compared with the traditional LS channel estimation method, the proposed method can improve the system error performance by 2~3 dB.