The recent discoveries of surprisingly large anomalous Hall effect (AHE) in antiferromagnets have attracted much attention due to their promising use in spintronics devices. However, such AHE‐hosting antiferromagnetic materials are rare in nature. Herein, it is demonstrated that Mn2.4Ga, a Fermi‐level‐tuned kagome antiferromagnet, has a large anomalous Hall conductivity of ≈150 Ω−1 cm−1 at room temperature that surpasses the usual high values (i.e., 20–50 Ω−1 cm−1) observed so far in two outstanding kagome antiferromagnets, Mn3Sn and Mn3Ge. Although the triangular spin structure of Mn2.4Ga shows a weak net magnetic moment of ≈0.05 µB per formula unit, it guarantees a nonzero Berry curvature in the kagome plane. Moreover, the anomalous Hall conductivity exhibits a sign reversal with the rotation of a small magnetic field that can be ascribed to the field‐controlled chirality of the spin triangular structure. This theoretical calculations further suggest that the large AHE in Mn2.4Ga originates from a significantly enhanced Berry curvature associated with the tuning of the Fermi level close to the Weyl points. These properties, together with the ability to manipulate moment orientations using a moderate external magnetic field, make Mn2.4Ga extremely exciting for future antiferromagnetic spintronics.