Based on delayed self-heterodyne and phase unwrapping techniques, a new approach to measure the frequency drift of a single-frequency laser by adopting relatively shorter fiber delay lines is proposed. The working principle and factors affecting the measurement accuracy of this method are given in theory. A laser that we can get the function of the frequency fluctuation easily is used to test the presented method. The experimental result demonstrates that the actual curve between laser frequency and time can be acquired accurately by this method. Then the frequency drift characteristic of a 1550 nm wavelength laser is measured by this method with a 6 m fiber delay line in 3 h continuously, resulting in the long-term frequency drift of 75 MHz/h, which is consistent basically with the nominal frequency stability 50 MHz/h.