The accurate attitude estimation of target ships plays a vital role in ensuring the safety of marine transportation, especially for tugs. A Light Detection and Ranging (LiDAR) system can generate 3D point clouds to describe the target ship’s geometric features that possess attitude information. In this work, the authors put forward a new attitude-estimation framework that first extracts the geometric features (i.e., the board-side plane of a ship) using point clouds from shipborne LiDAR and then computes the attitude that is of interest (i.e., yaw and roll in this paper). To extract the board-side plane accurately on a moving ship with sparse point clouds, an improved Random Sample Consensus (RANSAC) algorithm with a pre-processing normal vector-based filter was designed to exclude noise points. A real water-pool experiment and two numerical tests were carried out to demonstrate the accuracy and general applicability of the attitude estimation of target ships brought by the improved RANSAC and estimation framework. The experimental results show that the average mean absolute errors of the angle and angular-rate estimation are 0.4879 deg and 4.2197 deg/s, respectively, which are 92.93% and 75.36% more accurate than the estimation based on standard RANSAC.