Background: In many traits, not only individual trait levels are under genetic control, but also the variation around that level. In other words, genotypes do not only differ in mean, but also in (residual) variation around the genotypic mean. New statistical methods facilitate gaining knowledge on the genetic architecture of complex traits such as phenotypic variability. Here we study litter size (total number born) and its variation in a Large White pig population using a Double Hierarchical Generalized Linear model, and perform a genome-wide association study using a Bayesian method. Results: In total, 10 significant single nucleotide polymorphisms (SNPs) were detected for total number born (TNB) and 9 SNPs for variability of TNB (varTNB). Those SNPs explained 0.83% of genetic variance in TNB and 1.44% in varTNB. The most significant SNP for TNB was detected on 'Sus scrofa' chromosome (SSC) 11. A possible candidate gene for TNB is 'ENOX1', which is involved in cell growth and survival. On SSC7, two possible candidate genes for varTNB are located. The first gene is coding a swine heat shock protein 90 ('HSPCB = Hsp90'), which is a well-studied gene stabilizing morphological traits in 'Drosophila' and 'Arabidopsis'. The second gene is 'VEGFA', which is activated in angiogenesis and vasculogenesis in the fetus. Furthermore, the genetic correlation between additive genetic effects on TNB and on its variation was 0.49. This indicates that the current selection to increase TNB will also increase the varTNB. Conclusions: To the best of our knowledge, this is the first study reporting SNPs associated with variation of a trait in pigs. Detected genomic regions associated with varTNB can be used in genomic selection to decrease varTNB, which is highly desirable to avoid very small or very large litters in pigs. However, the percentage of variance explained by those regions was small. The SNPs detected in this study can be used as indication for regions in the 'Sus scrofa' genome involved in maintaining low variability of litter size, but further studies are needed to identify the causative loci.