An oscillator using a supply regulation loop and a method of operating the oscillator are provided. The oscillator includes a reference voltage generator configured to generate reference voltages from a supply voltage, a supply regulation loop circuit including a first operational amplifier and a transistor, the first operational amplifier being configured to receive a first reference voltage of the reference voltages, and the transistor being connected to an output terminal of the first operational amplifier, and a frequency locked loop (FLL) circuit configured to generate a clock signal, based on an input voltage determined based on a current flowing in the transistor and a second reference voltage of the reference voltages, wherein the first operational amplifier may include an input terminal configured to receive the first reference voltage and to receive negative feedback from the transistor, and the output terminal being configured to generate an output voltage independent of noise of the supply voltage.