The strong piezoelectric field in the InxGa1-xN/GaN quantum well (QW) LEDs, separates the electrons and holes spatially, which decreases the luminescence. Various shapes and compositions of such QWs are studied to improve the performance. We have studied the transition energy (TE), overlap of electron and hole wave functions, band structures and field distributions of the parabolic QWs (PQW) through the self consistent solutions of Schrodinger and Poisson equations. The shape of the PQW is varied along with the compositions and dopings. The square of the overlap of electron and hole wave functions i.e. the transition probability (TP) is strikingly increased, compared to the rectangular QW and it is even higher than the symmetrically staggered QW. At a particular current density, for the same TE, the TP of the PQW increases more than two times that of the rectangular QWs. An important feature, desirable for the QW LEDs emerge. The change of the TE with increase in the current density is minimized. A brief theory, computational procedures and the results will be presented in details with suitable discussions.