In recent years, artificial intelligence has played an important role on accelerating the whole process of drug discovery. Various of molecular representation schemes of different modals (e.g. textual sequence or graph) are developed. By digitally encoding them, different chemical information can be learned through corresponding network structures. Molecular graphs and Simplified Molecular Input Line Entry System (SMILES) are popular means for molecular representation learning in current. Previous works have done attempts by combining both of them to solve the problem of specific information loss in single-modal representation on various tasks. To further fusing such multi-modal imformation, the correspondence between learned chemical feature from different representation should be considered. To realize this, we propose a novel framework of molecular joint representation learning via Multi-Modal information of SMILES and molecular Graphs, called MMSG. We improve the self-attention mechanism by introducing bond level graph representation as attention bias in Transformer to reinforce feature correspondence between multi-modal information. We further propose a Bidirectional Message Communication Graph Neural Network (BMC GNN) to strengthen the information flow aggregated from graphs for further combination. Numerous experiments on public property prediction datasets have demonstrated the effectiveness of our model.