Genome-wide association studies (GWAS) have successfully discovered hundreds of associations between genetic variants and complex traits. Most GWAS have focused on the identification of single variants. It has been shown that most of the variants that were discovered by GWAS could only partially explain disease heritability. The explanation for this missing heritability is generally believed to be gene-gene (GG) or gene-environment (GE) interactions and other structural variants. Generalized multifactor dimensionality reduction (GMDR) has been proven to be reasonably powerful in detecting GG and GE interactions; however, its performance has been found to decline when outlying quantitative traits are present. This paper proposes a robust GMDR estimation method (based on the L-estimator and M-estimator estimation methods) in an attempt to reduce the effects caused by outlying traits. A comparison of robust GMDR with the original MDR based on simulation studies showed the former method to outperform the latter. The performance of robust GMDR is illustrated through a real GWA example consisting of 8,577 samples from the Korean population using the Homeostasis Model Assessment of Insulin Resistance (HOMA-IR) level as a phenotype. Robust GMDR identified the KCNH1 gene to have strong interaction effects with other genes on the function of insulin secretion.