Plane extraction is regarded as a necessary function that supports judgment basis in many applications, including semantic digital map reconstruction and path planning for unmanned ground vehicles. Owing to the heterogeneous density and unstructured spatial distribution of three-dimensional (3D) point clouds collected by light detection and ranging (LiDAR), plane extraction from it is recently a significant challenge. This paper proposed a parallel 3D Hough transform algorithm to realize rapid and precise plane detection from 3D LiDAR point clouds. After transforming all the 3D points from a Cartesian coordinate system to a pre-defined 3D Hough space, the generated Hough space is rasterised into a series of arranged cells to store the resided point counts into individual cells. A 3D connected component labeling algorithm is developed to cluster the cells with high values in Hough space into several clusters. The peaks from these clusters are extracted so that the targeting planar surfaces are obtained in polar coordinates. Because the laser beams emitted by LiDAR sensor holds several fixed angles, the collected 3D point clouds distribute as several horizontal and parallel circles in plane surfaces. This kind of horizontal and parallel circles mislead plane detecting results from horizontal wall surfaces to parallel planes. For detecting accurate plane parameters, this paper adopts a fraction-to-fraction method to gradually transform raw point clouds into a series of sub Hough space buffers. In our proposed planar detection algorithm, a graphic processing unit (GPU) programming technology is applied to speed up the calculation of 3D Hough space updating and peaks searching.