The dual-comb ranging system has shown great potential in the field of long-distance and high-precision measurement due to its fast measurement speed and high ranging accuracy. Usually, the complex hardware is required to lock the dual-comb system to ensure the stability of the system. This has a negative impact on the practical application of the dual-comb system. Therefore, the free-running dual-comb system is used as the light source, and the software correction algorithms (mainly the cross-ambiguity function) are used to extract the distance of the target, which greatly simplifies the complexity of the experimental system. The experimental results show that when the target distance is about 1 m, the laser repetition frequency is about 100 MHz, and the repetition frequency difference between the combs is about 774 Hz, the single-shot ranging accuracy of the free-running dual-comb system is about 3.56 m, and the measurement results have good linearity. This study has accumulated a certain foundation for the practical field application of the dual-comb system.