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 detailed 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^-12 at 1 s and the standard deviation is 1.5 mHz, which indicates the phase synchronization system can implement high-precision stabilization. This integrated stable laser comb should enable a wide range of applications beyond the laboratory.