An optically transparent on-glass frequency selective surface (FSS) is proposed with customized transmittivity of millimeter-wave (mm-wave) and sub-6G signals for 5G wireless communication. The presented FSS features a multi-resonant structure to selectively allow transmission of desired bands. With high optical transparency, the proposed FSS is formed through launching two metallic square loops and a hollowed patch onto a double-layer glass. Dual passbands covering 5G mm-wave n257/n258 and n260 bands are constructed, with sub-6G compatibility of an average in-band transmission of −2.42 dB. To verify the design principle, a proof-of-concept prototype is fabricated with an optical transparency of 62.1%. As experimental validation, transmission amplitudes above −3.2 dB are measured from 1.5 to 6 GHz, 23.5 to 30.7 GHz, and 36.1 to 40 GHz, with minimum insertion loss of 0.71 dB, 0.35 dB, and 0.97 dB, respectively, generally satisfying the requirement in 5G sub-6G, n257/n258, and n260 bands. The proposed approach delivers merits of bandpass filtering abilities across multiple 5G bands, high out-of-band rejection, high optical transparency, and low insertion loss, which may facilitate outdoor-to-indoor communication, confidential communication, and spectrum compatibility.