Cancer is one of the leading causes of death worldwide, which brings an urgent need for its effective treatment. However, cancer is highly heterogeneous, meaning that one cancer can be divided into several subtypes with distinct pathogenesis and outcomes. This is considered as the main problem which limits the precision treatment of cancer. Thus, cancer subtypes identification is of great importance for cancer diagnosis and treatment. In this work, we propose a deep learning method which is based on multi-omics and attention mechanism to effectively identify cancer subtypes. We first used similarity network fusion to integrate multi-omics data to construct a similarity graph. Then, the similarity graph and the feature matrix of the patient are input into a graph autoencoder composed of a graph attention network and omics-level attention mechanism to learn embedding representation. The K-means clustering method is applied to the embedding representation to identify cancer subtypes. The experiment on eight TCGA datasets confirmed that our proposed method performs better for cancer subtypes identification when compared with the other state-of-the-art methods. The source codes of our method are available at https://github.com/kataomoi7/multiGATAE.