The present work systematically discusses the planar-feature-based registration method of high-precision fusion of terrestrial LiDAR point clouds, wherein unit quaternion is used as the description operator of spatial rotation transformation. The 4-tuple representation method of planar features in three-dimensional (3D) space is given first. Then, the planar feature-based spatial similarity transformation model is constructed on the basis of ensuring the uniqueness of those planar features' mathematical expressions. Using the parameter equivalent of each conjugate planar features after registration as the constraint condition, the objective function of the 3D spatial similarity transformation is constructed according to the least square criterion, and the iterative solution of the registration parameters is analyzed according to the extremum of the function. Finally, the correctness and effectiveness of the algorithm are verified by two sets of LiDAR point cloud data. Results show that in solving the spatial similarity transformation parameters, the 4-tuple expression method of planar features is used in judging the consistency of the same-name features after registration through the condition constraints of the parameter equivalent. Simultaneously, the two constraints of normal consistency and distance zero between the same-name plane features are considered. Introducing quaternion makes the expressions of the spatial similarity transformation model more concise, and there are fewer additional constraints in during registration. In the experimental scheme, given any initial value of an unknown parameter, the proposed algorithm can run and get correct results.