Chirped pulse spectral interferometry is a commonly used continuous and high time-resolved diagnostic instrument, however, its applications in the fields of ultrafast and large timescales physics are constrained by the relationship between time resolution and test range. Utilizing linearly-chirped pulse series and a recording system of a spectrometer coupled streak camera, a scanning spectrum laser interferometer is designed. To demonstrate the feasibility, principle of the interferometer is studied theoretically and numerically. It is concluded that the scanning spectrum laser interferometer could measure phase perturbation signal accurately, and possesses the same time resolution and several times test range compared to chirped pulse spectral interferometry. Additionally, in the recording system, the influence of sampling intervals on the measurement results of the scanning spectrum laser interferometer is numerically analyzed. The results show that the influence could be ignored while raw data are clean, but if noise is contained, the measurement errors would increase gradually with the sampling intervals decreasing.