The Mathematic model of bit synchronization charge-pump Phase Locked Loop (PLL) is presented which takes into account the aperiodic reference pulses and the leakage current of the loop filter. We derive theoreitcal static phase error, overload and stability of bit synchronization charge-pump PLL using presented model and compare it with one of the conventional charge-pump PLL model. We can analysis bit synchronization charge-pump PLL exactly because our model takes into account the leakage current of the loop filter and aperiodic input data which are the charateristics of bit synchronization charge-pump PLL. We also verify it using HSPICE simulation with a bity synchronizer circuit.