Multiple response regression model is commonly employed to investigate the relationship between multiple outcomes and a set of potential predictors, where single-response analysis and multivariate analysis of variance (MANOVA) are two frequently used methods for association analysis. However, both methods have their own limitations. The basis of the former method is independence of multiple responses and the latter one assumes that multiple responses are normally distributed. In this work, the authors propose a test statistic for multiple response association analysis in high-dimensional situations based on F statistic. It is free of normal distribution assumption and the asymptotic normal distribution is obtained under some regular conditions. Extensive computer simulations and four real data applications show its superiority over single-response analysis and MANOVA methods.