As one of the most promising alternatives to internal combustion engine vehicles, battery electric vehicles (BEVs) have become increasingly prevalent in recent years. However, range anxiety is still a major concern among BEV users or potential users in recent years. The social-psychological factors were found to be associated with range anxiety, but how the charging decisions are affected by range anxiety is still unclear. Thus, in our study, through an online questionnaire issued in mainland China, we collected 230 participants' charging decisions in 60 range-anxiety-inducing scenarios in which both distance-related, and time-related anxiety co-existed. Then, an interpretable machine learning (ML) approach with the Shapley Additive Explanations method was used to model BEV users' charging decisions in these scenarios. To further explore users' decision-making mechanisms, a Bayesian-Network-regression mixed approach was used to model the inner topological structure among the factors influencing users' decisions. We find that both time-related and distance-related factors can affect users' charging decisions, but the influence of waiting time is softer compared to the BEV range. Users' charging decisions can also be moderated by users' psychological states (i.e., range anxiety level and trust in range estimation system), individual differences (i.e., age and personality), and BEV using experience (i.e., driving mileage, display mileage and range estimation cycle of range estimation system), of which, the range anxiety level is more directly related with users' charging decisions. Findings from this study can provide insights into the optimization of charge station distribution and customization of the charging recommendation system.