The characteristics of laser power spectra under different laser linewidths are investigated experimentally based on the fiber-delayed acousto-optic modulator (AOM) shifted self-heterodyne scheme, and the relevant simulation analysis is performed. Meanwhile, a simple method is introduced that short fiber is used to measure the linewidth of a narrow-linewidth laser. When the delay time of the fiber is less than the coherence time of the laser, 3 dB width of the beat signal cannot be directly used for measuring the laser linewidth. The experimental and theoretical analysis shows that the measurement result is hardly affected by the narrow peak. Therefore, it should be considered that the oscillations of the wings of the power spectrum rather than the effects of the narrow peak when dealing with the data. Using the weighted least square method, the laser linewidth can be obtained by theoretically fitting the experimental heterodyne spectrum. The scheme is not affected by the limit of the minimum resolution of the system, and it is applicable to the laser linewidth measurement, especially for narrow-linewidth lasers.