Although genome-wide association studies (GWAS) often collect data on multiple correlated traits for complex diseases, conventional gene-based analysis is usually univariate, and therefore, treating traits as uncorrelated. Multivariate analysis of multiple correlated traits can potentially increase the power to detect genes that affect some or all of these traits. In this study, we propose the multivariate hierarchically structured variable selection (HSVS-M) model, a flexible Bayesian model that tests the association of a gene with multiple correlated traits. With only summary statistics, HSVS-M can account for the correlations among genetic variants and among traits simultaneously and can also estimate the various directions and magnitudes of associations between a gene and multiple traits. Simulation studies show that HSVS-M substantially outperforms competing methods in various scenarios, particularly when variants in a gene are associated with a trait in similar directions and magnitudes. We applied HSVS-M to the summary statistics of a meta-analysis GWAS on four lipid traits from the Global Lipids Genetics Consortium and identified 15 genes that have also been confirmed as risk factors in previous studies.