An oscillator having a modulation function capable of controlling a frequency by adding a signal to a control signal and a PLL circuit using the same, wherein the oscillator forms a ring comprised of a plurality of cascade connected delay stages controlled in delay value by an inverter or a buffer and a control signal and forming a closed loop by an inverted phase and comprises a modulation function modulating an oscillation frequency by adding a modulation signal to the control signal in a part of the plurality of delay stages.