Microwave photonic pulse generation has intrinsic high speed and large bandwidth, and it can overcome the sampling-rate limitation in the electrical domain. Herein, we propose a partly temporally-overlapped photon echo scheme to generate microwave pulses with a high data transfer rate and precision pulse width. The partly overlapped chirped control pulse has the same chirped rate segments but different time delays. The time delay between the segments and the number of segments can be adjusted to achieve a controllable multipulse photon echo train. We developed a theoretical model based on the photon echo process and performed simulations to obtain nonlinear chirped periodic spectral grating in a Tm3+:YAG crystal and gave the time delay provided by the spectral grating to the probe pulse at different instantaneous frequencies. We further generated pulse code modulation signals to verify the performance of the target signal. The proposed signal-generation scheme has potential applications in microwave photonics and modern radar systems.