In single-shot, ultrafast time-resolved measurements, the combination of linear chirp pulse and spectrometer is a common way. In this paper, according to the time-frequency mapping relationship of linear chirp pulse and utilizing an imaging spectrometer as a recording system, we design a chirped pulse velocity interferometer for the ultrafast measurement of free surface velocity. Theoretical research on the principle and applicability shows that picosecond resolution is achievable and the velocity sensitivity is easily adjustable, which greatly widens applications of the velocity interferometer. The numerical simulation of the measurement process shows that reconstructed velocity signal is well consistent with the given velocity, further confirming the feasibility of the chirped pulse velocity interferometer.