We developed an all-polarization-maintaining, polarization-multiplexed, dual-comb fiber laser with a nonlinear amplifying loop mirror (NALM) mode-locking mechanism. Owing to the use of the slow and fast axes of a polarization-maintaining fiber (PMF), the dual-frequency combs with slightly different repetition rates from the single-laser cavity are generated at the same center wavelength without extra-cavity nonlinear spectral broadening. The narrow relative beat note between the two frequency combs is obtained with a full-width-at-half-maximum of ~1 kHz in the optical frequency domain. The two frequency combs have high relative stability and mutual coherence owing to passive common-mode noise cancellation.