The electronic structure of linear homocatenated indium (In) polymer has been studied by tight-binding band calculations with the extended Huckel approximation. The polymer was found to have semiconducting behavior with a direct gap. The highest occupied crystal orbital (HOCO) of the polymer are formed by sigma-bonding between neighboring p orbitals of In atoms, whose sigma-electrons were well delocalized along the main chain. The possible presence of sigma-conjugation in the chains can result in sigma-sigma* interband transitions, as in the case of polysilane, which is formed by group 14 elements.