In this letter, we develop an effective algorithm for direction-of-arrival (DOA) estimation of coherent signals in the presence of direction-dependent mutual coupling. Based on the structure feature of mutual coupling matrix, we firstly eliminate the mutual coupling effect by selecting the middle subarray outputs. Subsequently, we exploit a linear combination of the subarray manifolds to formulate forward/backward linear prediction models. Finally, the DOAs of coherent signals are extracted from the phase factors of the roots that make the prediction polynomial to be zero. Without any array calibration, the proposed algorithm can accurately estimate the DOAs of coherent signals under direction-dependent mutual coupling. Numerical results demonstrate the effectiveness of the proposed algorithm.