Non-destructive and accurate inspection of gallium nitride light-emitting diode (GaN-LED) epitaxial wafers is important to GaN-LED technology. However, the conventional electroluminescence inspection, the photoluminescence inspection, and the automated optical inspection cannot fulfill the complex technical requirements. In this work, an inspection method and an operation system based on soft single-contact operation, namely, single-contact electroluminescence (SC-EL) inspection, are proposed. The key component of the SC-EL inspection system is a soft conductive probe with an optical fiber inside, and an AC voltage (70$V_{\mathrm{pp}}$, 100 kHz) is applied between the probe and the ITO electrode under the LED epitaxial wafer. The proposed SC-EL inspection can measure both the electrical and optical parameters of the LED epitaxial wafer at the same time, while not causing mechanical damage to the LED epitaxial wafer. Moreover, it is demonstrated that the SC-EL inspection has a higher electroluminescence wavelength accuracy than photoluminescence inspection. The results show that the non-uniformity of SC-EL inspection is 444.64%, which is much lower than that of photoluminescence inspection. In addition, the obtained electrical parameters from SC-EL can reflect the reverse leakage current ($I_s$) level of the LED epitaxial wafer. The proposed SC-EL inspection can ensure high inspection accuracy without causing damage to the LED epitaxial wafer, which holds promising application in LED technology.