When there is multipath propagation, the spatial spectrum direction-finding performance of circular arrays will be severely degraded. To address this, an algorithm based on the central symmetric array for smooth spatial spectrum estimation on a moving platform is proposed. This algorithm utilizes the spatial translation of the array to obtain multiple translated covariance matrices; at the same time, it leverages the symmetry of the central symmetric array to process the received data in reverse, obtaining the covariance matrix of the virtual array data. Subsequently, by stacking all covariance matrices, a new full-rank covariance matrix can be obtained, which achieves de-correlation processing and completes the estimation of the signal's direction of arrival. Simulation experiments have verified the effectiveness of this method and it has significant value for engineering applications.