Provided is an Inductor-Capacitor (LC) quadrature Voltage Controlled Oscillator (VCO) having a startup circuit which can accurately select one of +90° and −90° as a phase difference between two clocks generated by the LC quadrature VCO by embodying the startup circuit therein by using a phase detector and a controller. The LC quadrature VCO includes a first LC tank for generating a second clock signal and a fourth clock signal, a second LC tank for generating a first clock signal and a third clock signal, a phase detector for receiving the clock signals from the first LC tank and the second LC tank, and detecting whether a phase difference between the clocks is +90° or −90°, and a controller for discriminating whether phase information detected by the phase detector is equivalent to a phase difference between clocks required by the external signal processing unit, and changing an operation mode of the first LC tank and/or the second LC tank on the basis of the discrimination result of the phase difference between the clocks.