Due to the advancement in high throughput technologies and robust experimental designs, many recent studies attempt to incorporate heterogeneous data obtained from multiple technologies to improve our understanding of the molecular dynamics associated with biological processes. Currently available technologies produce wide variety of large amount of data spanning from genomics, transcriptomics, proteomics, and epigenetics. Due to the fact that such multi-omics data are very diverse and come from different biological levels, it has been a major research challenge to develop a model to properly integrate all available and relevant data to advance biomedical research. It has been argued by many researchers that the integration of multi-omics data to extract relevant biological information is currently one of the major biomedical informatics challenges. This paper proposes a new graph database model to efficiently store and mine multi-omics data. We show a working model of this graph database with transcriptomics, genomics, epigenetics and clinical data for three cancer types from the Cancer Genome Atlas. Moreover, we highlight the usefulness of graph database mining to extract relevant biological interpretations and also to find novel relationships between different data levels.