Potential applications of terahertz (THz) radiation are constantly being investigated for high-speed communication due to its large bandwidth. For example, frequency hopping communication technology would benefit from the large bandwidth. To attach the information to the carrier wave, THz modulators with deep and stable modulation at different frequencies are crucial, yet are still lacking. Here a THz modulator, designed by integrating a non-resonant field enhancement effect of periodic metal microslits to assist a Fabry-Perot resonance structure (MS-FP) is proposed and demonstrated. New equations are developed to describe the superior performance of the novel design. The >95% modulation depth is achieved by a SiO2/Si gated graphene device at 14 Fabry-Perot resonant frequencies across 1.4 THz bandwidth, outperforming the recently reported 75% modulation depth THz modulator with a similar Fabry-Perot structure. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement