In this letter, we propose a novel algorithm to estimate the direction-of-arrival (DOA) for coherent signals exploiting the moving coprime array (MCA). Firstly, we construct a decoherent covariance matrix by utilizing the data vectors received at specific time instants, whose structure is similar to that of the covariance matrix under the condition of uncorrelated signals. Then we use vectorization, array interpolation and matrix completion technologies to reconstruct the data vector received by the augmented uniform linear array (ULA). Afterwards, forward/backward spatial smoothing (FBSS) and root-MUSIC are applied for DOA estimation. Simulation results demonstrate the effectiveness and superiority of the proposed algorithm when processing coherent signals.