ABSTRACT The capacity to accurately predict an individual’s phenotype from their DNA sequence is one of the great promises of genomics and precision medicine. Recently, Bayesian methods for generating polygenic predictors have been successfully applied in human genomics but require the individual level data, which are often limited in their access due to privacy or logistical concerns, and are computationally very intensive. This has motivated methodological frameworks that utilise publicly available genome-wide association studies (GWAS) summary data, which now for some traits include results from greater than a million individuals. In this study, we extend the established summary statistics methodological framework to include a class of point-normal mixture prior Bayesian regression models, which have been shown to generate optimal genetic predictions and can perform heritability estimation, variant mapping and estimate the distribution of the genetic effects. In a wide range of simulations and cross-validation using 10 real quantitative traits and 1.1 million variants on 350,000 individuals from the UK Biobank (UKB), we establish that our summary based method, SBayesR, performs similarly to methods that use the individual level data and outperforms other state-of-the-art summary statistics methods in terms of prediction accuracy and heritability estimation at a fraction of the computational resources. We generate polygenic predictors for body mass index and height in two independent data sets and show that by exploiting summary statistics on 1.1 million variants from the largest GWAS meta-analysis ( n ≈ 700, 000) that the SBayesR prediction R 2 improved on average across traits by 6.8% relative to that estimated from an individual-level data BayesR analysis of data from the UKB ( n ≈ 450, 000). Compared with commonly used state-of-the-art summary-based methods, SBayesR improved the prediction R 2 by 4.1% relative to LDpred and by 28.7% relative to clumping and p -value thresholding. SBayesR gave comparable prediction accuracy to the recent RSS method, which has a similar model, but at a computational time that is two orders of magnitude smaller. The methodology is implemented in a very efficient and user-friendly software tool titled GCTB.