Although genome-wide association studies (GWASs) have identified many risk loci for complex traits and common diseases, most of the identified associations reside in noncoding regions and have unknown biological functions. Recent genomic sequencing studies have produced a rich resource of annotations that help characterize the function of genetic variants. Integrative analysis that incorporates these functional annotations into GWAS can help elucidate the biological mechanisms underlying the identified associations and help prioritize causal-variants. Here, we develop a novel, flexible Bayesian variable selection model with efficient computational techniques for such integrative analysis. Different from previous approaches, our method models the effect-size distribution and probability of causality for variants with different annotations and jointly models genome-wide variants to account for linkage disequilibrium (LD), thus prioritizing associations based on the quantification of the annotations and allowing for multiple causal-variants per locus. Our efficient computational algorithm dramatically improves both computational speed and posterior sampling convergence by taking advantage of the block-wise LD structures of human genomes. With simulations, we show that our method accurately quantifies the functional enrichment and performs more powerful for identifying true causal-variants than several competing methods. The power gain brought up by our method is especially apparent in cases when multiple causal-variants in LD reside in the same locus. We also apply our method for an in-depth GWAS of age-related macular degeneration with 33,976 individuals and 9,857,286 variants. We find the strongest enrichment for causality among non-synonymous variants (54x more likely to be causal, 1.4x larger effect-sizes) and variants in active promoter (7.8x more likely, 1.4x larger effect-sizes), as well as identify 5 potentially novel loci in addition to the 32 known AMD risk loci. In conclusion, our method is shown to efficiently integrate functional information in GWASs, helping identify causal-variants and underlying biology.