We report the discovery of CaMn2Al10, a metal with strong magnetic anisotropy and moderate electronic correlations. Magnetization measurements find a Curie-Weiss moment of 0.83 µB/Mn, significantly reduced from the Hund's rule value, and the magnetic entropy obtained from specific heat measurements is correspondingly small, only ≈ 9 % of Rln 2. These results imply that the Mn magnetism is highly itinerant, a conclusion supported by density functional theory calculations that find strong Mn-Al hybridization. Consistent with the layered nature of the crystal structure, the magnetic susceptibility χ is anisotropic below 20 K, with a maximum ratio of χ [010] /χ [001] ≈ 3.5. A strong power-law divergence χ(T ) ∼ T −1.2 below 20 K implies incipient ferromagnetic order, and an Arrott plot analysis of the magnetization suggests a vanishingly low Curie temperature TC ∼ 0. Our experiments indicate that CaMn2Al10 is a rare example of a Mn-based weak itinerant magnet that is poised on the verge of ferromagnetic order.