As an indispensable infrastructure for the future life, smart grid is being implemented to save energy, reduce costs and increase reliability. In smart grid, control center networks have attracted a great number of attentions, because their security and dependability issues are critical to the entire smart grid. Several studies have been conducted in the field of security, but few work focuses on the dependability analysis of control center networks. In this paper, we adopt a concise mathematic tool, stochastic Petri nets (SPNs), to analyze the dependability of control center networks in smart grid. With the proposed SPNs model, we can measure the dependability from two metrics, i.e., the reliability and availability, through analyzing the transient probability. We also study a specific case to demonstrate the feasibility and efficiency of the proposed model in the dependability analysis of control center networks in smart grid.