MOTIVATION: Testing the association between multiple phenotypes with a set of genetic variants simultaneously, rather than analyzing one trait at a time, is receiving increasing attention for its high statistical power and easy explanation on pleiotropic effects. The kernel-based association test (KAT), being free of data dimensions and structures, has proven to be a good alternative method for genetic association analysis with multiple phenotypes. However, KAT suffers from substantial power loss when multiple phenotypes have moderate to strong correlations. To handle this issue, we propose a maximum KAT (MaxKAT) and suggest using the generalized extreme value distribution to calculate its statistical significance under the null hypothesis. RESULTS: We show that MaxKAT reduces computational intensity greatly while maintaining high accuracy. Extensive simulations demonstrate that MaxKAT can properly control type I error rates and obtain remarkably higher power than KAT under most of the considered scenarios. Application to a porcine dataset used in biomedical experiments of human disease further illustrates its practical utility. AVAILABILITY AND IMPLEMENTATION: The R package MaxKAT that implements the proposed method is available on Github https://github.com/WangJJ-xrk/MaxKAT.