Emotion recognition plays an essential role in interpersonal communication. However, existing recognition systems use only features of a single modality for emotion recognition, ignoring the interaction of information from the different modalities. Therefore, in our study, we propose a global-aware Cross-modal feature Fusion Network (GCF2-Net) for recognizing emotion. We construct a residual cross-modal fusion attention module (ResCMFA) to fuse information from multiple modalities and design a global-aware module to capture global details. More specifically, we first use transfer learning to extract wav2vec 2.0 features and text features fused by the ResCMFA module. Then, cross-modal fusion features are fed into the global-aware module to capture the most essential emotional information globally. Finally, the experiment results have shown that our proposed method has significant advantages than state-of-the-art methods on the IEMOCAP and MELD datasets, respectively.