Summary: In this paper, renormalization of bandgap energy in V-shaped quantum wires has been considered. We have constructed a possible mechanism, in the framework of random phase approximation, for calculation of screened Coulomb potential and the value of the renormalized gap energy. Two possible candidates for this form of confinement potential have been considered and a mathematical framework for computation of bandgap renormalization in each case is presented. Some numerical calculations for screened potential and value of gap renormalization have been performed and in each case these results have been described.