With the rapid development of multi-omics technologies and accumulation of large-scale bio-datasets, many studies have conducted a more comprehensive understanding of human diseases and drug sensitivity from multiple biomolecules, such as DNA, RNA, proteins and metabolites. Using single omics data is difficult to systematically and comprehensively analyze the complex disease pathology and drug pharmacology. The molecularly targeted therapy-based approaches face some challenges, such as insufficient target gene labeling ability, and no clear targets for non-specific chemotherapeutic drugs. Consequently, the integrated analysis of multi-omics data has become a new direction for scientists to explore the mechanism of disease and drug. However, the available drug sensitivity prediction models based on multi-omics data still have problems such as overfitting, lack of interpretability, difficulties in integrating heterogeneous data, and the prediction accuracy needs to be improved. In this paper, we proposed a novel drug sensitivity prediction (NDSP) model based on deep learning and similarity network fusion approaches, which extracts drug targets using an improved sparse principal component analysis (SPCA) method for each omics data, and construct sample similarity networks based on the sparse feature matrices. Furthermore, the fused similarity networks are put into a deep neural network for training, which greatly reduces the data dimensionality and weakens the risk of overfitting problem. We use three omics of data, RNA sequence, copy number aberration and methylation, and select 35 drugs from Genomics of Drug Sensitivity in Cancer (GDSC) for experiments, including Food and Drug Administration (FDA)-approved targeted drugs, FDA-unapproved targeted drugs and non-specific therapies. Compared with some current deep learning methods, our proposed method can extract highly interpretable biological features to achieve highly accurate sensitivity prediction of targeted and non-specific cancer drugs, which is beneficial for the development of precision oncology beyond targeted therapy.