Brain glycogen synthase kinase-3 (GSK3) is hyperactive in several neurological conditions that involve impairments in both cognition and neurogenesis. This raises the hypotheses that hyperactive GSK3 may directly contribute to impaired cognition, and that this may be related to deficiencies in neural precursor cells (NPC). To study the effects of hyperactive GSK3 in the absence of disease influences, we compared adult hippocampal NPC proliferation and performance in three cognitive tasks in male and female wild-type (WT) mice and GSK3 knockin mice, which express constitutively active GSK3. NPC proliferation was ~40% deficient in both male and female GSK3 knockin mice compared with WT mice. Environmental enrichment (EE) increased NPC proliferation in male, but not female, GSK3 knockin mice and WT mice. Male and female GSK3 knockin mice exhibited impairments in novel object recognition, temporal order memory, and coordinate spatial processing compared with gender-matched WT mice. EE restored impaired novel object recognition and temporal ordering in both sexes of GSK3 knockin mice, indicating that this repair was not dependent on NPC proliferation, which was not increased by EE in female GSK3 knockin mice. Acute 1 h pretreatment with the GSK3 inhibitor TDZD-8 also improved novel object recognition and temporal ordering in male and female GSK3 knockin mice. These findings demonstrate that hyperactive GSK3 is sufficient to impair adult hippocampal NPC proliferation and to impair performance in three cognitive tasks in both male and female mice, but these changes in NPC proliferation do not directly regulate novel object recognition and temporal ordering tasks.