High penetration of electric vehicles (EVs) as moving loads in power system have drawn increasing concerns about their negative impacts. Due to the spatial-temporal random dynamics of EVs, it is a challenge for identification and positioning of the space and time varying impacts. Most previous studies investigated system-wide EV charging demand based on data analysis with deterministic charging location and time. In this circumstance, this paper proposes a probabilistic model for nodal charging demand based on the spatial-temporal dynamics of moving EVs. Following the introduction to the integrated system with graph theory, a spatial-temporal model of moving EV loads is established based on random trip chain and Markov decision process (MDP). The nodal EV charging demands are derived from the charging probabilities of single and multiple EVs. The system studies show that this model is capable to assess the nodal charging demand due to the spatial-temporal distribution of moving EVs.