This paper studies the exciton-longitudinal-optical-phonon coupling in InGaN/GaN single quantum wells with various cap layer thicknesses by low temperature photoluminescence (PL) measurements. With increasing cap layer thickness, the PL peak energy shifts to lower energy and the coupling strength between the exciton and longitudinal-optical (LO) phonon, described by Huang-Rhys factor, increases remarkably due to an enhancement of the inteal electric field. With increasing excitation intensity, the zero-phonon peak shows a blueshift and the Huang-Rhys factor decreases. These results reveal that there is a large built-in electric field in the well layer and the exciton-LO-phonon coupling is strongly affected by the thickness of the cap layer.