Spatial aliasing and spatial resolution are the two issues faced by most multiple speech source localization methods. The histogram of time delays is a simple but effective method to deal with these two issues on linear arrays. But few methods were capable of applying the time delay histogram to directional-of-arrivals (DOAs) estimation using a planar array. This paper proposes a novel method to estimate DOAs of multiple speech sources based on time delay histograms across all microphones of a planar array. The pairwise time delays of different sources are firstly obtained from each time delay histogram, and then, the time delays are identified with variant speech sources. Eventually, the DOA of each source is estimated by regression over its associated time delays. We conducted some experiments in both simulated and real environments to evaluate the proposed method using an eight-element circular array. The experimental results confirmed not only its high computational efficiency, but also its superiority in spatial resolution and spatial anti-aliasing.