Phase difference regression (PDR) was widely utilized to estimate Direction-of-Arrival (DOA) for linear arrays because of its high time resolution and high computational efficiency. However, conventional regression methods were seldom reported to estimate DOA using planar arrays. This paper proposes a regression method to derive DOA from all phase differences on all frequencies for a planar array. The DOA is represented as the function of the array topology and phase differences between all microphones. Moreover, the proposed method considers another two problems that were often ignored by most regression methods. One is the problem about the period of phase difference in the regression cost function. The other is the signal enhancement that can effectively suppress the acoustic interference. We conducted some experiments in simulated environment to evaluate the proposed method using a 9-element circular array. The experimental results confirmed its superiority in both computational efficiency and robustness.