The influence of free evolution time on the Ramsey signal characteristics of a pulsed optically pumped Rb clock based on a compact magnetron microwave cavity was reported, and in addition, the effect of coherence relaxation time on the contrast of clock signal was discussed. When the optimal free evolution time of the atomic clock is about 3 ms, the Ramsey central fringe contrast is as high as 52% and the shot-noise-limit is better than 1.7×10－14(τ=1 s). According to the contrast of the Ramsey signal and the optical density in the vapor cell, both population and coherence relaxation times of Rb vapor cell in the atomic clock are 1.95 ms and 2.45 ms, respectively. The experiment provides a useful basis for improving the performance of the pulsed optically pumped Rb clock.