A simple generalized theory is presented for the determination of interband optical absorption coefficient (IOAC) around band edges, in quantum well (QW) structure of non-parabolic semiconducting materials whose band structures obey the three band model of Kane. The dependence of absorption coefficient on wave-vector (k⃗) has also been investigated. IOAC has been calculated for a wide range of III–V compound semiconductors, such as InAs, InSb, Hg1-xCdxTe, and In1-xGaxAsyP1-y lattice matched to InP. It has been found that IOAC for QWs increases in steps with increasing photon energy and the positions of jumps of the coefficient are more closely spaced in the three band model of Kane than those with parabolic energy band approximations in all the cases. IOAC for QWs is largely dependent on the polarization direction of the incident light and on the well dimension as well. The expressions of IOAC presented in this article can easily be extended to incorporate the effects of different external conditions like strain, electric, and magnetic fields on IOAC. It has also been shown that under certain limiting conditions the expressions for IOAC reduces to the previously known results for wide band gap materials and this is the indication for it to be a generalized theory for IOAC.