We used a bivariate animal model to investigate the genetic correlations between yield traits or days open (DO) as characters measured in cows and semen production traits as characters measured in bulls. Lactation records of 305-day milk, fat, and protein yields, and DO, from 386 809 first-lactation Holstein cows in Hokkaido, Japan, that calved between 2008 and 2014 were used. Semen production records were collected between 2005 and 2014 and included volume per ejaculate (VOL), sperm concentration (CON), number of sperm per ejaculate (NUM), progressive motility index of sperm (MOT), and MOT after freeze-thawing (A-MOT). Number of sperm per ejaculate was log-transformed into a NUM score (NUMS). A total of 30 373 semen production records from 1196 bulls were obtained. The pedigree file used for analysing the records was involving 885 345 animals. Heritability was estimated for VOL (0.42), CON (0.12), NUMS (0.37), MOT (0.08), and A-MOT (0.11). Weak and negative genetic correlations were recorded between yield traits measured in cows and VOL, CON or NUMS measured in bulls. Moderate and negative genetic correlations were obtained between DO and MOT (–0.42) or A-MOT (–0.43). Selection focused on MOT or A-MOT measured in bulls may therefore improve DO measured in cows.