A metamaterial based on complementary planar double-split-ring resonator (DSRR) structure is presented and demonstrated, which can optically tune the transmission of the terahertz (THz) wave. Unlike the traditional DSRR metamaterials, the DSRR discussed in this paper consists of two split rings connected by two bridges. Numerical simulations with the finite-difference time-domain (FDTD) method reveal that the transmission spectra of the original and the complementary metamaterials are both in good agreement with Babinet’s principle. Then by increasing the carrier density of the intrinsic GaAs substrate, the magnetic response of the complementary special DSRR metamaterial can be weakened or even turned off. This metamaterial structure is promised to be a narrow-band THz modulator with response time of several nanoseconds.