The magnetic phase diagram of a polar ferrimagnet CaBaFe 4 O 7 with a magnetic easy axis has been investigated by measurements of magnetization, specific heat, and magnetoelectricity. A ferrimagnetic transition takes place at T C1 = 275 K within the orthorhombic phase followed by a second magnetic transition at T C2 = 211 K. Below T C2 , successive metamagnetic transitions occur for magnetic fields applied perpendicular to the easy axis, implying a sequential emergence of magnetic states which are neither collinear nor coplanar. The observation of the static magnetoelectric effect was limited to temperatures below 120 K due to the conducting nature of the crystals at higher temperatures. The magnitude of the ferroelectric polarization shows large changes between the different field-induced magnetic phases. The low-field state is characterized by a large linear magnetoelectric coefficient of α cc = 39 ps/m, while a gigantic polarization change of P = 850 μC/m 2 is observed for μ o H = 14 T applied along the easy axis.