An InGaN/GaN multiple quantum well (MQW) structure is grown on a GaN/sapphire template using a plasma-assisted molecular beam epitaxy (PA-MBE). The fluctuation of the quantum well thickness formed from roughly-grown InGaN layer results in a disordered photoluminescence (PL) spectrum. The surface morphologies of the InGaN layers with various In compositions are investigated by reflection high energy electron diffraction (RHEED) and atomic force microscopy (AFM). A blurred InGaN/GaN hetero-interface and the non-uniform QW size is confirmed by high resolution transmission electron microscopy (HR-TEM). Inhomogeneity of the quantum confinement results in a degradation of the quantum efficiency even though the InGaN layer has a uniform In composition.