To date, thousands of genetic variants to be associated with numerous human traits and diseases have been identified by genome-wide association studies (GWASs). The GWASs focus on testing the association between single trait and genetic variants. However, the analysis of multiple traits and single nucleotide polymorphisms (SNPs) might reflect physiological process of complex diseases and the corresponding study is called pleiotropy association analysis. Modern day GWASs report only summary statistics instead of individual-level phenotype and genotype data to avoid logistical and privacy issues. Existing methods for combining multiple phenotypes GWAS summary statistics mainly focus on low-dimensional phenotypes while lose power in high-dimensional cases. To overcome this defect, we propose two kinds of truncated tests to combine multiple phenotypes summary statistics. Extensive simulations show that the proposed methods are robust and powerful when the dimension of the phenotypes is high and only part of the phenotypes are associated with the SNPs. We apply the proposed methods to blood cytokines data collected from Finnish population. Results show that the proposed tests can identify additional genetic markers that are missed by single trait analysis. © 2020 Wiley Periodicals LLC.