TTFF (Time-To-First-Fix) is an important indicator of GPS receiver performance, and must be reduced as much as possible. Bit synchronization is the pre-condition of positioning, which affects TTFF. The frequency error leads to power loss, which makes it difficult to find the bit edge. The conventional bit synchronization methods only work well when there is no or very small frequency error. The bit synchronization process is generally carried out after the pull-in stage, where the carrier loop is already stable. In this paper, a new bit synchronization method based on frequency compensation is proposed. Through compensating the frequency error, the new method reduces the signal power loss caused by the accumulation of coherent integration. The performances of the new method in different frequency error scenarios are compared. The parameters in the proposed method are analyzed and optimized to reduce the computational complexity. Simulation results show that the new method has good performance when the frequency error is less than 25Hz. Test results show that the new method can tolerate dynamic frequency errors, and it is possible to move the bit synchronization to the pull-in process to reduce the TTFF.