Transcriptome-wide association analysis is a powerful approach to studying the genetic architecture of complex traits. A key component of this approach is to build a model to predict gene expression levels from genotypes from samples with matched genotypes and expression in a specific tissue. However, it is challenging to develop robust and accurate imputation models with limited sample sizes for any single tissue. Here, we first introduce a multi-task learning approach to jointly impute gene expression in 44 human tissues. Compared with single-tissue methods, our approach achieved an average 39% improvement in imputation accuracy and generated effective imputation models for an average 120% more genes in each tissue. We then describe a summary statistic-based testing framework that combines multiple single-tissue associations into a single powerful metric to quantify overall gene-trait association at the organism level. Applying to analyze genome wide association results for 50 complex traits, we were able to identify considerably more genes in tissues enriched for trait heritability, and cross-tissue analysis significantly outperformed single-tissue strategies.