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Point cloud registration refers to a critical step in point cloud preprocessing, which aims to uniformly represent the objects expressed by the two point sets. To solve spatial discrepancies in the collected artificial building point clouds, this study develops a point cloud registration method by employing dual quaternion description based on the point-linear feature constraint. First, the spatial transformation parameters are expressed by the dual quaternion, and the rotation matrix and translation vector are expressed simultaneously to avoid the error of separate calculations from accumulating. Subsequently, the registration model is built by complying with the constraints of coordinate equivalence after the registration of the same-name points, parallelism of direction vectors after registration of the same-name lines and the spatial geometric relationship between points and lines. On that basis, the scale factor is considered to register point clouds at different scales. Second, an optimized Levenberg–Marquardt method is adopted to solve the registration model for avoiding the iterative non-convergence attributed to inappropriate initial values in the solution. Lastly, the robustness and reliability exhibited by the proposed method are verified by performing two experiments with the simulated and measured data. As indicated from the experimentally achieved results, the joint constraint of point-linear features can achieve higher accuracy than the constraint of point or line features independently, and the combined point-linear features can register point clouds in high quality when point cloud data are scaled and partially missing. This study presents an effective registration method for manually registered auxiliary targets when they are difficult to deploy. [ABSTRACT FROM AUTHOR]