Many human diseases involve multiple genes in complex interactions. Large Genome-Wide Association Studies (GWASs) have been considered to hold promise for unraveling such interactions. However, statistic tests for high-order epistatic interactions ( $\mathrm{⩾}\mathrm{2}$ Single Nucleotide Polymorphisms (SNPs)) raise enormous computational and analytical challenges. It is well known that the block-wise structure exists in the human genome due to Linkage Disequilibrium (LD) between adjacent SNPs. In this paper, we propose a novel Bayesian method, named BAM, for simultaneously partitioning SNPs into LD-blocks and detecting genome-wide multi-locus epistatic interactions that are associated with multiple diseases. Experimental results on the simulated datasets demonstrate that BAM is powerful and efficient. We also applied BAM on two GWAS datasets from WTCCC, i.e., Rheumatoid Arthritis and Type 1 Diabetes, and accurately recovered the LD-block structure. Therefore, we believe that BAM is suitable and efficient for the full-scale analysis of multi-disease-related interactions in GWASs.