Abstract Background Knowledge on the levels of linkage disequilibrium (LD) across the genome, persistence of gametic phase between breed pairs, genetic diversity and population structure are important parameters for the successful implementation of genomic selection. Therefore, the objectives of this study were to investigate these parameters in order to assess the feasibility of a multi-herd and multi-breed training population for genomic selection in important purebred and crossbred pig populations in Canada. A total of 3,057 animals, representative of the national populations, were genotyped with the Illumina Porcine SNP60 BeadChip (62,163 markers). Results The overall LD ( r 2 ) between adjacent SNPs was 0.49, 0.38, 0.40 and 0.31 for Duroc, Landrace, Yorkshire and Crossbred (Landrace x Yorkshire) populations, respectively. The highest correlation of phase (r) across breeds was observed between Crossbred animals and either Landrace or Yorkshire breeds, in which r was approximately 0.80 at 1 Mbp of distance. Landrace and Yorkshire breeds presented r ≥ 0.80 in distances up to 0.1 Mbp, while Duroc breed showed r ≥ 0.80 for distances up to 0.03 Mbp with all other populations. The persistence of phase across herds were strong for all breeds, with r ≥ 0.80 up to 1.81 Mbp for Yorkshire, 1.20 Mbp for Duroc, and 0.70 Mbp for Landrace. The first two principal components clearly discriminate all the breeds. Similar levels of genetic diversity were observed among all breed groups. The current effective population size was equal to 75 for Duroc and 92 for both Landrace and Yorkshire. Conclusions An overview of population structure, LD decay, demographic history and inbreeding of important pig breeds in Canada was presented. The rate of LD decay for the three Canadian pig breeds indicates that genomic selection can be successfully implemented within breeds with the current 60 K SNP panel. The use of a multi-breed training population involving Landrace and Yorkshire to estimate the genomic breeding values of crossbred animals (Landrace × Yorkshire) should be further evaluated. The lower correlation of phase at short distances between Duroc and the other breeds indicates that a denser panel may be required for the use of a multi-breed training population including Duroc.