A self-complementary metasurface is presented for application in multiband terahertz filters. The unit cell structures of the self-complementary metasurface consist of a combination of an ordinary Jerusalem cross and its complementary counterpart that resonates in the THz regime. The columnar repetition of ordinary and complementary resonator structures enables complementary spectral responses for incident waves with mutually orthogonal linear polarizations. The operating principles of the self-complementary metamaterial with the interaction between the juxtaposed ordinary and complementary Jerusalem crosses are explained using an equivalent circuit method and are confirmed with a full-wave electromagnetic simulation. The designed self-complementary metasurface functions as a selective bandstop filter (BSF) or bandpass filter (BPF) depending on the polarization states of the incident wave. The fabricated metasurface exhibits high polarization purity, exemplified by a polarization extinction ratio as high as 24 dB. The transmittance phases of the two orthogonally polarized waves have phase differences between -73° and 83° within a broad frequency range.