This paper describes the design of a 32 Gb/s four-level pulse amplitude modulation (PAM-4) optical transceiver in a 40 nm CMOS technology. At the transmitter side, the laser driver is composed of an asymmetric waveform equalizer, a 3-tap feed-forward equalizer (FFE), and a novel active-back termination (ABT) circuit. The ABT circuit provides a self-tracking, tunable source impedance to match the characteristic impedance of different laser diodes. At the receiver side, the fully integrated optical receiver consists of a transimpedance amplifier, a variable gain amplifier, an automatic threshold tracking circuit (ATC), and a quarter-rate decision feedback equalizer (DFE). By using the adaptive ATC, it reduces the BER induced by the harmonic distortion along the signal path by more than 27X. Both the ATC and DFE are automatically adapted by an on-chip sign-sign LMS (SSLMS) engine. Fabricated in TSMC 40 nm CMOS process, the chip area for the transmitter and receiver are about 0.029 mm2 and 0.23 mm2. The power consumptions are about 146.8 mW and 128.8 mW respectively for the PAM-4 transmitter and receiver.