Left-right asymmetry is known to exist at several anatomical levels in the brain and recent studies have provided further evidence to show that it also exists at a molecular level in the hippocampal CA3-CA1 circuit. The distribution of N-methyl-d-aspartate (NMDA) receptor NR2B subunits in the apical and basal synapses of CA1 pyramidal neurons is asymmetrical if the input arrives from the left or right CA3 pyramidal neurons. In the present study, we examined the role of hippocampal asymmetry in cognitive function using β2-microglobulin knock-out (β2m KO) mice, which lack hippocampal asymmetry. We tested β2m KO mice in a series of spatial and non-spatial learning tasks and compared the performances of β2m KO and C57BL6/J wild-type (WT) mice. The β2m KO mice appeared normal in both spatial reference memory and spatial working memory tasks but they took more time than WT mice in learning the two non-spatial learning tasks (i.e., a differential reinforcement of lower rates of behavior (DRL) task and a straight runway task). The β2m KO mice also showed less precision in their response timing in the DRL task and showed weaker spontaneous recovery during extinction in the straight runway task. These results indicate that hippocampal asymmetry is important for certain characteristics of non-spatial learning.