Selecting reliable beacon nodes plays a significant role in relocalizing unknown nodes in a wireless sensor network. When the position of a beacon node is drifted or is spoofed, it becomes an unreliable beacon node, which would lead to a large relocalization deviation of unknown nodes in its neighbor. However, when selecting reliable beacon nodes, most relocalization algorithms only screen either drifting beacon nodes or malicious beacon nodes whose position is drifted or spoofed. This article proposes an algorithm that can simultaneously screen drifting beacon nodes and malicious beacon nodes. The algorithm is divided into four steps. First, three indicators are introduced, where two are for describing position drifting and one is for describing position spoofing. Second, the entropy method is used to weight the contributions of three indicators. Third, a technique for order preference by similarity to an ideal solution is used to construct a reliability evaluation model. Finally, using the reliability evaluation model select reliable beacon nodes. Experimental results illustrate that the detection accuracy of drifting beacon nodes and malicious beacon nodes of the proposed algorithm is 7.5% and 8.2% higher than that of the state-of-the-art algorithms, respectively.