We model carrier-density-dependent radiative and non-radiative recombination rates in an InGaN/GaN quantum well structure containing a V-pit and a threading dislocation. It is known that the threading dislocation acts as the nonradiative recombination center, leading to the reduction of carriers which can participate in the radiative recombination. On the other hand, the quantum well structure grown on the sidewalls of V-pit, formed by the strain relying on In/Ga contents and connected with threading dislocation directed along the polar direction, plays a role of energy barriers to prevent quantum well in-plane charge carriers from flowing to the non-radiative recombination center, i.e., the threading dislocation. Therefore, such V-pits can enhance the internal quantum efficiency in the InGaN/GaN quantum well light emitting diode (LED). However, the explicit model of the V-pit and the threading dislocation coupled to three dimensional electronic states has rarely been studied. We take into account those defects by including their potentials in a system Hamiltonian. It can describe the electronic states of in-plane quantum well, in which a V-pit and a threading dislocation are positioned. Here we show that charged carriers are more distributed away from the threading dislocation by having the V-pit, and it leads to the reduction of carrier losses to the non-radiative recombination and hence the enhancement of radiative recombination rate. Their effects on the recombination rates depend on injected carrier densities. We also discuss mid-gap defect states, which may be generated due to the threading dislocation and the V-pit.