The combination of multiple drugs is a significant therapeutic strategy that can enhance treatment effectiveness and reduce medication side effects. However, identifying effective synergistic drug combinations in a vast search space remains challenging. Current methods for predicting synergistic drug combinations primarily rely on calculating drug similarity based on the drug heterogeneous network or drug information, enabling the prediction of pairwise synergistic drug combinations. However, these methods not only fail to fully study the rich information in drug heterogeneous networks, but also can only predict pairwise drug combinations. To address these limitations, we present a novel Synergistic Multi-drug Combination prediction method of Western medicine based on Heterogeneous Network representation learning with Contrastive Learning, called SMC-HNCL. Specifically, two drug features are learnt from different perspectives using the drug heterogeneous network and anatomical therapeutic chemical (ATC) codes, and fused by attention mechanism. Furthermore, a group representation method based on multi-head self-attention is employed to learn representations of drug combinations, innovatively realizing the prediction of synergistic multi-drug combinations. Experimental results demonstrate that SMC-HNCL outperforms the state-of-the-art baseline methods in predicting synergistic drug pairs on two synergistic drug combination datasets and can also effectively predict synergistic multi-drug combinations.