The interrupted transmitting and receiving (ITR) can be used in anechoic chamber to solve the coupling between the transmitted and reflected signals. When the ITR periods are random, the fake peaks in high resolution range profile (HRRP) of ITR echo can be reduced. Then, by utilizing the piecewise sparse property of ITR echo, the HRRP is reconstructed based on compressive sensing (CS). However, the periods of ITR determine the restricted isometry property (RIP) condition and the HRRP reconstruction performance. In order to improve the HRRP reconstruction performance, the ITR periods sequence optimization method based on genetic algorithm (GA) is proposed in this paper. The correlation coefficient of the sensing matrix columns is minimized after optimization so that the RIP of sensing matrix can be well satisfied. Simulation and comparison results illustrate that the optimization method converges fast and the HRRP reconstruction performance is improved with the optimized ITR periods.