We proposed a novel strategy to design a deep subwavelength metasurface with full 2π transmission phase modulation and high transmission efficiency by applying resonators with interfering Fano resonance. Theoretical investigation demonstrates that the transmission efficiency of the resonators depends on the direct transmission coefficient, direct reflection coefficient, and Q factor. When an impedance layer is added in the resonators, the direct transmission and direct reflection coefficients can be facilely manipulated so that the span of the transmission phase around the resonance frequency can be extended to 2π. As a result, we can continuously adjust the transmission phase from 0 to 2π through changing the geometric parameters of the resonators and construct a deep subwavelength metasurface with the resonators to manipulate the transmission wave with high efficiency. We also find that a layer of grating can be used as the impedance layer to change direct transmission and direct reflection in the actual design of the metasurface. The proposed strategy may provide effective guidance to design a deep subwavelength metasurface for controlling a transmitted wave with high efficiency.