Microwave-to-optical phase synchronization techniques have attracted growing research interests in recent years.Here,we demonstrate tight,real-time phase synchronization of an optical frequency comb to a rubidium atomic clock.A de-tailed mathematical model of the phase locking system is developed to optimize its built-in parameters.Based on the model,we fabricate a phase locking circuit with high integration.Once synchronized,the fractional frequency instability of the repetition rate agrees to 6.35×10-12at 1 s and the standard deviation is 1.5 mHz,which indicates the phase syn-chronization system can implement high-precision stabilization.This integrated stable laser comb should enable a wide range of applications beyond the laboratory.