We have developed a high-sensitivity tune measurement system based on diode detection for an electron storage ring, and we have carried out the tune measurement without beam excitation on the Hefei Light Source-II (HLS-II) storage ring. In this paper, we present in detail the design of the developed system for the HLS-II storage ring, and have carried out the simulations and experiments. The developed system is mainly composed of the analog front-end (AFE), spectrum analyzer, and host computer. We verified the performance of the AFE by simulation and offline experiment. In the experiment, we employed the host computer for real-time observation of the tune. As a result, the online experiments of the developed system on the HLS-II storage ring show a good signal-to-noise ratio of about 25 dB in the top-off mode without beam excitation. Compared with the conventional tune measurement system of the electron storage ring, the advantages of our system are its simple structure, low cost, and no beam excitation is required.