Under ideal clean atmosphere conditions, the backscatter signal intensity of micro-pulse lidar has a monotonic variation with height. An inversion algorithm of cloud vertical structure based on the interpolation and reconstruction method is proposed to screen the corresponding interpolation points in the pre-processed signal for Akima interpolation, with the places with the lowest and highest detection distances as the starting point and reference point, respectively. The obtained forward and backward reconstructed signals are further averaged to simulate the cloud-free signal. Clouds and aerosols are first distinguished by the proposed algorithm combining the adaptative threshold and empirical threshold to determine the candidate cloud interval. On this basis, the intensity of the simulated cloud-free signal is compared with that of the pre-processed signal, and the cloud base and cloud top heights of the candidate clouds are extracted. The validation using micro-pulse lidar data shows that compared with the results of the traditional direct inversion algorithm, the correlation coefficients of the cloud base and cloud top are improved to 0.9836 and 0.9334, and the root mean square errors are reduced to 43.8 m and 280.2 m, which indicates that the proposed method effectively improves the accuracy of cloud detection.