The multiple signal classification method for direction-of-arrival estimation is widely applied in practical scenarios. However, the multiple signal classification method with planar array requires 2-dimensional on-grid spectrum searches, which would lead to the grid mismatch and high computational complexity. Therefore, a high-precision fast direction-of-arrival estimation method for planar array is proposed. In the proposed method, a 2-stage grid search approach over the 2-dimensional spectrum is firstly applied to obtain a quick coarse estimation of direction of arrival. Then, the estimation of higher precision is achieved via a quadratic surface fitting method. Simulation results verified the effectiveness of the proposed method.