The high-speed railway (HSR) surveying system in China has developed into a modern large-scale precision surveying system with multi-stage structure, large scale, and high precision and reliability requirements. The effective control of the surveying data quality in each stage and each link is a complex but important issue in the processing of surveying data. However, as an important part of surveying system, the study on the data quality control of vertical control network has not attracted as much attention as that of plane control network. Constrained adjustment is the essential link of surveying data processing of HSR vertical control network to obtain the height of new control points. Before that, in addition to the gross errors checking of observations, the compatibility diagnosis of datum points should also be an important step, which is often neglected in practice. In this paper, the likelihood ratio (LR) test with the highest power among all the competitors for simple hypotheses problem is extended to solve the problem of composite hypothesis, resulting in a new multiple incompatible datum points identification strategy (ICDPI-LR). With a benchmark along route control network and a CPIII vertical control network as the example, the performance of the proposed method is demonstrated, and showing the importance and necessity of the identification of incompatible datum points in vertical control network for HSR.