A multi-behavior aware service recommendation method based on hypergraph graph convolutional neural network (MBSRHGNN) was proposed to resolve the problem of insufficient high-order service feature extraction in existing service recommendation methods. A multi-hypergraph was constructed according to user-service interaction types and service mashups. A dual-channel hypergraph convolutional network was designed based on the spectral decomposition theory with functional and structural properties of multi-hypergraph. Chebyshev polynomial was used to approximate hypergraph convolution kernel to reduce computational complexity. Self-attention mechanism and multi-behavior recommendation methods were combined to measure the importance difference between multi-behavior interactions during the hypergraph convolution process. A hypergraph pooling method named HG-DiffPool was proposed to reduce the feature dimensionality. The probability distribution for recommending different services was learned by integrating service embedding vector and hypergraph signals. Real service data was obtained by the crawler and used to construct datasets with different sparsity for experiments. Experimental results showed that the MBSRHGNN method could adapt to recommendation scenario with highly sparse data, and was superior to the existing baseline methods in accuracy and relevance.