A continuous-time graph signal can be viewed as a time series of graph signals. It generalizes both the classical continuous-time signal and ordinary graph signal. Therefore, such a signal can be considered as a function on two domains: the graph domain and the time domain. In this paper, we consider the sampling theory of bandlimited continuous-time graph signals. To formulate the sampling problem, we need to consider the interaction between the graph and time domains. We describe an explicit procedure to determine a discrete sampling set for perfect signal recovery. Moreover, in analogous to the Nyquist-Shannon sampling theorem, we give an explicit formula for the minimal sample rate.