We propose a method (fastBAT) that performs a fast set-based association analysis for human complex traits using summary-level data from genome-wide association studies (GWAS) and linkage disequilibrium (LD) data from a reference sample with individual-level genotypes. We demonstrate using simulations and analyses of real datasets that fastBAT is more accurate and orders of magnitude faster than the prevailing methods. Using fastBAT, we analyze summary data from the latest meta-analyses of GWAS on 150,064-339,224 individuals for height, body mass index (BMI), and schizophrenia. We identify 6 novel gene loci for height, 2 for BMI, and 3 for schizophrenia at PfastBAT < 5 × 10(-8). The gain of power is due to multiple small independent association signals at these loci (e.g. the THRB and FOXP1 loci for schizophrenia). The method is general and can be applied to GWAS data for all complex traits and diseases in humans and to such data in other species.