A dither-free Quad- and Null-bias point locking scheme for Mach-Zehnder (MZ) silicon optical modulators is presented. In this scheme, a pair of differential monitoring photodetectors (MPDs) (an inphase-MPD in the same phase as the output and an outerphase-MPD with a 180° phase difference to the output) are used as the signal feedback components for closing-loop control. The ratio of the inphase-MPD current to the outerphase-MPD current is denoted as the normalized photocurrent, which is then used to construct the error functions for the Quad point (90° phase bias) and the Null point (180° phase bias). For Quad point locking, the error function is the difference between the normalized photocurrent and the responsivity ratio of the inphase-MPD and outerphase-MPD. For Null point locking, the error function is the first derivative of the normalized photocurrent relative to the thermal power bias point of the thermo-optic phase shifter, and the adjustment direction of the bias power is determined by the positive or negative sign of the second derivative. Then, the theoretical expression of the algorithm is derived according to the theoretical model of the MZ silicon optical modulator, and the proposed algorithm is verified by simulation. The verification results are in agreement with the conclusions of the mathematical derivation formula. Finally, a 53 GBaud 4-level pulse amplitude modulation (PAM4) test platform and a 53 GBaud binary phase-shift keying (BPSK) simulation platform are built to validate the accuracy of the proposed algorithm in Quad and Null point locking for MZ silicon optical modulators.