A new frequency selective surface (FSS) and its complementary structure are proposed in this paper. The design structures have features of dual band stopband and dual band passband responses, being intended to work in the terahertz (THz) range. The unit cell of the FSS consists of an enhanced capacitance-loaded Jerusalem cross (JC) and an outer square loop resonator (SLR). Two resonances of the bandstop FSS are centered at 0.23 and 0.36 THz with 10 dB stopband bandwidths (BWs) of 16.5 % and 17.1 % respectively. The designed FSS provides excellent angular stability up to an incidence angle of 80°. The complementary geometry of the designed FSS exhibits dual passband characteristics. The 3 dB passband BW (S21 > -3 dB) covers the frequencies 0.18-0.25 THz and 0.31-0.45 THz. The unit cell has a periodicity of 245 μ m or 0.19 λL, where λL is the wavelength at the lower resonance frequency. © 2022 IEEE.