This report includes the first sibling study of mouse behavior, and presents evidence for a heritable general cognitive ability (g) factor influencing cognitive batteries. Data from a population of male and female outbred mice (n = 84), and a replication study of male sibling pairs (n = 167) are reported. Arenas employed were the T-maze, the Morris water maze, the puzzle box, the Hebb-Williams maze, object exploration, a water plus-maze, and a second food-puzzle arena. The results show a factor structure consistent with the presence of g in mice. Employing one score per arena, this factor accounts for 41% of the variance in the first study (or 36% after sex regression) and 23% in the second, where this factor also showed sibling correlations of 0.17-0.21, which translates into an upper-limit heritability estimate of around 40%. Reliabilities of many tasks are low and consequently set an even lower ceiling for inter-arena or sibling correlations. Nevertheless, the factor structure is seen to remain fairly robust across permutations of the battery composition and the current findings fit well with other recent studies.