In past years, there has been significant progress in the field of indoor robot localization. To precisely recover the position, the robots usually relies on multiple on-board sensors. Nevertheless, this affects the overall system cost and increases computation. In this research work, we considered a light detection and ranging (LiDAR) device as the only sensor for detecting surroundings and propose an efficient indoor localization algorithm. To attenuate the computation effort and preserve localization robustness, a weighted parallel iterative closed point (WP-ICP) with interpolation is presented. As compared to the traditional ICP, the point cloud is first processed to extract corners and line features before applying point registration. Later, points labeled as corners are only matched with the corner candidates. Similarly, points labeled as lines are only matched with the lines candidates. Moreover, their ICP confidence levels are also fused in the algorithm, which make the pose estimation less sensitive to environment uncertainties. The proposed WP-ICP architecture reduces the probability of mismatch and thereby reduces the ICP iterations. Finally, based on given well-constructed indoor layouts, experiment comparisons are carried out under both clean and perturbed environments. It is shown that the proposed method is effective in significantly reducing computation effort and is simultaneously able to preserve localization precision.