Strong magneto-optical effect of Zn1-xCoxO near the optical band gap is reported. Magnetic circular dichroism (MCD) and Faraday rotation of Zn1-xCoxO (x = 0.012 and 0.016) at 5 K are as high as 2°/cm Oe at 3.4 eV, which are about two orders larger than those of ZnO. Absence of strong Co2+ d-d* transition near the optical band gap makes Zn1-xCoxO an useful material for short-wavelength magneto-optical applications. Large magneto-optical effects and paramagnetic temperature dependence of MCD show a strong mixing of the sp bands of the host ZnO with Co2+ d orbitals. The polarity of the MCD peak is negative indicating the antiferromagnetic p-d exchange interaction.