In a fibre-optic interferometer, when the frequency linewidth of the light source is larger than a certain value, the influence of optical fibre dispersion should be considered. In this paper, considering the dispersion effect, we present a theoretical analysis of the output noise power spectrum of the fibre-optic interferometer induced by the random phase noise of semiconductor lasers. The analysis focuses on the noise power spectrum influenced by the first-order dispersion of the single-mode optical fibre. The closed expressions of output noise characteristics are derived. The formulations obtained in this paper can be applied to both a dispersion and a non-dispersion fibre-optic interferometer or optical interferometer.