DNA methylation data-based precision tumour early diagnostics is emerging as the state of the art for molecular tumour recognition, which could capture the signals of cancer occurrence 3 ~ 5 years in advance and clinically more homogenous groups. However, the sensitive of early detection for many tumors is about 30%, which needs to be greatly improved. Nevertheless, on the basis of the whole genome bisulfite sequencing methylation data, a comprehensive characterisation of the entire molecular genetic landscape of the tumor as well as the subtle differences between different tumours could be identified. With the accumulation of methylation data, high performance deep learning models that considering and modeling more unbiased information need to be developed. According to the above analysis, we designed a pipeline to investigate genome-wide DNA methylation patterns for precision multi-tumour early diagnostics. We proposed a graph convolutional network considering the attention mechanism to dissect DNA methylation heterogeneity of different cancer types. The attention mechanism in the graph convolutional network architecture could detect the cancer signals from genome-wide methylated molecular interactions, improving the robustness and sensitivity of multi-tumor classification. Experimental results demonstrates the feasibility of precision multi-tumour early diagnostics with the DNA methylation data. The workflow presented here is very useful for tumor classification, which highly relevant for the future blood diagnosis and treatment of the tumour.