Tissue-specific splicing of exons plays an important role in determining tissue identity. However, computational tools predicting tissue-specific effects of variants on splicing are lacking. To address this issue, we developed MTSplice (Multi-tissue Splicing), a neural network which quantitatively predicts effects of human genetic variants on splicing of cassette exons in 56 tissues. MTSplice combines the state-of-the-art predictor MMSplice, which models constitutive regulatory sequences, with a new neural network which models tissue-specific regulatory sequences. MTSplice outperforms MMSplice on predicting effects associated with naturally occurring genetic variants in most tissues of the GTEx dataset. Furthermore, MTSplice predicts that autism-associated de novo mutations are enriched for variants affecting splicing specifically in the brain. MTSplice is provided free of use and open source at the model repository Kipoi. We foresee MTSplice to be useful for functional prediction and prioritization of variants associated with tissue-specific disorders.