At present, we have achieved a very high modulation depth, but it is unable to realize wave shaping for the lack of research on tunable modulation depth. On the basis of electrical tuning of graphene and the resonance property of graphene metamaterial surface plasmon polaritons (SPP), a graphene metamaterial modulator of tunable modulation depth at a frequency is proposed and the modulation depth is the maximum value, which is convenient for sampling and testing. The transmission law is theoretically analyzed by using the harmonic oscillator model. Based on the simulation of three-dimensional simulation software time domain solver, the series of modulation depth corresponding to the frequency of 11.85 THz is obtained, where the maximum modulation depth is greater than 96%. The series of the modulation depth can be modulated and transformed by bias voltage regulating graphene Fermi level. This will greatly promote the application of modulator in the wave shaping, such as generating sine wave, triangle wave and square wave. In addition, this structure can achieve a similar electromagnetically induced transparency (EIT) phenomenon. It can not only achieve the frequency shift and the transmission peak broadening, but also keep the center frequency the same before and after broading center frequency.