Slow wave and localized field are conducive to terahertz (THz) modulators with deep and fast modulation. Here we propose an electrically controlled THz modulator with slow wave effect and localized field composed of a high electron mobility transistor (HEMT) integrated metasurface. Unlike previously proposed schemes to realize slow wave effect electrically, this proposal controls the resonant modes directly through HEMT switches instead of the surrounding materials, leading to a modulation depth of 96% and a group delay of 10.4ps. The confined electric field where HEMT is embedded, and the slow wave effect, work together to pave a new mechanism for THz modulators with high performance.