A time dilation drift tube is simulated by Particle-In-Cell(PIC) model, which can be used for measuring pulsed signal at least 10 ps for Full Width at Half Maximum(FWHM). The factors influencing the coefficient of spread are calculated including radius of photocathode, length of acceleration tube, acceleration voltage, length of drift tube, center magnetic field of solenoid，energy and current of photo electrons. Results show that a linear characteristic exists between the coefficient of spread and the energy and current of photo electrons, which means signal of time dilation drift tube is independent of initial pulsed electrons energy distribution and current waveform. The proposed time dilation drift tube offers a way to diagnose beam length parameter of inverse Compton scattering source instead of streak camera.