We describe a high-precision ranging method based on an optical balanced cross-correlation system with a scanning repetition rate using a single femtosecond laser. By scanning the repetition rate of a laser, measuring pulses can be overlapped with reference pulses. It is an effective method to make reference pulses overlap with coaxial multiple target pulses without additional mechanical devices. The overlapped pulses are launched to the optical balanced cross-correlation system, which improves the time resolution measurement to the attosecond level. Two nominal distances are measured, and an additional commercial laser interferometer is used as a comparison to evaluate the accuracy of our measurement system. Moreover, the thickness of three stacked glasses is measured by our measurement system to verify that this system can measure coaxial multiple targets more quickly than conventional optical balanced cross-correlation systems using a single optical frequency comb.