A relaxation oscillator for generating a first and a second oscillation signals, comprising: a reference-voltage providing circuit for providing a high and a low reference voltages; switches for directing the high and low reference voltages to inputs of a transconductance amplifier and a non-inverting input of a comparator; the transconductance amplifier for generating an output current with a value determined by its transconductance value, controlled by an input tuning voltage, and multiplied by its inputs' voltage difference; a capacitor connecting between the transconductance amplifier output and ground; and the comparator for generating a first and a second digital signals; wherein the first and second digital signals are digital control signals to the switches, and the first and second oscillation signal of the relaxation oscillator respectively; wherein the oscillation frequency of the relaxation oscillator is independent of the reference voltages, achieving accurate frequency turning, and simplifying the reference-voltage providing circuit.