A single-cavity multi-comb fiber laser based on multi-dimensional pulse multiplexing transmission was proposed by combining wavelength multiplexing, polarization multiplexing and direction multiplexing. Polarization-maintaining fibers and inline polarizers were placed on different branches of bidirectional fiber lasers to realize polarization multiplexing mechanism based on birefringence effect and spectral filtering effect based on Lyot. Dual-comb, tri-comb and quad-comb generation could be realized by adjusting the pump powers, laser polarization states and intracavity loss of lasers. Based on the single-cavity tri-comb laser, the envelope of the beat frequency signals of obtained interferogram was extracted by using the Hilbert-transform algorithm, and the absolute distance measurement of 2 km single-mode fiber was realized according to the optical vernier effect. The ranging results coincide with the results by using standard optical time-domain reflectometer, which verifies the good coherence between the optical combs. This scheme provides a low-complexity multi-comb light source, which has the potential to be used in multi-comb precision measurement field.