Spin Hall nano-oscillators (SHNOs) exploiting current-driven magnetization auto-oscillation have recently received much attention because of their potential for neuromorphic computing. Widespread applications of neuromorphic devices with SHNOs require an energy-efficient method of tuning oscillation frequency over broad ranges and storing trained frequencies in SHNOs without the need for additional memory circuitry. While the voltage-driven frequency tuning of SHNOs has been demonstrated, it was volatile and limited to megahertz ranges. Here, we show that the frequency of SHNOs is controlled up to 2.1 GHz by an electric field of 1.25 MV/cm. The large frequency tuning is attributed to the voltage-controlled magnetic anisotropy (VCMA) in a perpendicularly magnetized Ta/Pt/[Co/Ni]n/Co/AlOx structure. Moreover, the non-volatile VCMA effect enables cumulative control of the frequency using repetitive voltage pulses which mimic the potentiation and depression functions of biological synapses. Our results suggest that the voltage-driven frequency tuning of SHNOs facilitates the development of energy-efficient neuromorphic devices.