Point cloud registration is a crucial task in fields such as three-dimensional reconstruction, target localization, and simultaneous localization and mapping. In the case of relatively low overlap, points out of the overlapping region act as interferences that will have a terrible impact on the registration results. Some existing registration methods improved for low-overlap situations still suffer from poor accuracy and low success rate. Therefore, a reliable two-stage registration method is introduced. First, a quality first sample consensus algorithm is used to determine the initial points for optimal transport and complete the coarse registration. Second, a reliable optimal transport algorithm is proposed for fine registration, in which the points for transmission are dynamically adjusted according to the iteration of the transport plan to improve the registration efficiency. In the registration experiments with the standard models and real scene models, this method reached 1e−02 and 1e−01 orders of magnitude, respectively, which outperforms better than the existing mainstream algorithms. This method can still perform excellent and stable registration results on multiple models and various missing cases, and the success rate is kept at more than 90%.