In this letter, a compressive sampling system, which can acquire chirp signal without the prior information of carrier frequency and chirp rate, is proposed. The system first estimates the chirp rate based on windowed modulated wideband converter (MWC). When chirp rate is derived, the system can de-chirp the target signal. Then, the de-chirped signal is acquired by sampling module of the system. Finally, basedon samples, the original signal can be reconstructed by a greedy iteration algorithm which has an adaptive halting condition. Simulation results show the system is capable of estimating chirp rate and reconstructing original signal.