Deep learning techniques have been widely used for power system operations as a very hot topic in recent years. This paper proposed a spatiotemporal deep learning-based low frequency oscillation mode estimation method using synchrophasor data. The proposed deep learning method consists of the graph convolutional network (GCN) and the long short-term memory (LSTM). A graph network is used to model the power network in which the edges represent the connection relationships between system buses. Specifically, the GCN method is used to capture the topological structure of the power networks to obtain the spatial dependence. The LSTM model is used to capture the dynamic change of electrical variables that can be monitored by PMU devices through synchrophasor data to obtain the temporal dependence. Eventually, the proposed GCN-LSTM model is used to capture the spatiotemporal patterns and features of the system-wide synchrophasor data. To validate the effectiveness of the proposed method, we evaluate it on two classic IEEE simulation platform, i.e., IEEE 39-bus system and IEEE 118-bus system, by comparing with the Nonlinear Autoregressive Neural Network with External Input (NARX), the Gated Recurrent Unit (GRU) network, and single LSTM methods. It is demonstrated that the proposed GCN-LSTM method can achieve the best estimation results for different simulation platforms.