Abnormally active glycogen synthase kinase‐3 (GSK3) contributes to pathological processes in multiple psychiatric and neurological disorders. Modeled in mice, this includes increasing susceptibility to dysregulation of mood‐relevant behaviors, impairing performance in several cognitive tasks and impairing adult hippocampal neural precursor cell (NPC) proliferation. These deficits are all evident in GSK3α/β knockin mice, in which serine‐to‐alanine mutations block the inhibitory serine phosphorylation regulation of both GSK3 isoforms, leaving GSK3 hyperactive. It was unknown if both GSK3 isoforms perform redundant actions in these processes, or if hyperactivity of one GSK3 isoform has a predominant effect. To test this, we examined GSK3α or GSK3β knockin mice in which only one isoform was mutated to a hyperactive form. Only GSK3β, not GSK3α, knockin mice displayed heightened vulnerability to the learned helplessness model of depression‐like behavior. Three cognitive measures impaired in GSK3α/β knockin mice showed differential regulation by GSK3 isoforms. Novel object recognition was impaired in GSK3β, not in GSK3α, knockin mice, whereas temporal order memory was not impaired in GSK3α or GSK3β knockin mice, and co‐ordinate spatial processing was impaired in both GSK3α and GSK3β knockin mice. Adult hippocampal NPC proliferation was severely impaired in GSK3β knockin mice, but not impaired in GSK3α knockin mice. Increased activity of GSK3β, in the absence of overexpression or disease pathology, is sufficient to impair mood regulation, novel object recognition and hippocampal NPC proliferation, whereas hyperactive GSK3α individually does not impair these processes. These results show that hyperactivity of the two GSK3 isoforms execute non‐redundant effects on these processes.