Photodissociation cross sections of H₂⁺ by the electronic transition from the bound 1s sigma _g state to the continuum of the weakly bound 2p pi _u state have been calculated over the accessible range of wavelengths lambda lambda 500-1200 AA. The partial cross sections sigma _{nu j} obtained for all the vibrational levels ( nu =0-18) and the rotational level J=1 were summed over nu with an appropriate weighting factor rho _{nu J} to get the total cross section sigma . The cross section sigma for the 1s sigma _g to 2p pi _u transition was found to be much larger than that for the 1s sigma _g to 2p sigma _u transition over the range of wavelengths lambda lambda approximately 600-1000 AA. Special features of the sigma to pi transition are discussed.