Emotion recognition in conversation (ERC) has attracted much attention in recent years for its necessity in widespread applications. Existing ERC methods mostly model the self and inter-speaker context separately, posing a major issue for lacking enough interaction between them. In this paper, we propose a novel Speaker and Position-Aware Graph neural network model for ERC (S+PAGE), which contains three stages to combine the benefits of both Transformer and relational graph convolution network (R-GCN) for better contextual modeling. Firstly, a two-stream conversational Transformer is presented to extract the coarse self and inter-speaker contextual features for each utterance. Then, a speaker and position-aware conversation graph is constructed, and we propose an enhanced R-GCN model, called PAG, to refine the coarse features guided by a relative positional encoding. Finally, both of the features from the former two stages are input into a conditional random field layer to model the emotion transfer. Extensive experiments demonstrate that our model achieves state-of-the-art performance on three ERC datasets.