We experimentally explored the influence of passive harmonic mode locking on the temporal and spectral features of a ytterbium-doped fiber laser. Similar dependences of free-running linewidth of the laser carrier-envelope offset frequency (f0) on the intracavity net dispersion were observed for the fundamental-, second-, and third-order mode-locking states. Due to the reduction of nonlinear effects and supermode phase locking that balanced the third-order dispersion in the fiber cavity, the third-order harmonic mode-locking exhibited the narrowest free-running f0 linewidth of ~120 kHz in the near-zero net dispersion regime.