This paper proposes a novel quadrature VCO(QVCO) based on direct back-gate second harmonic coupling. The QVCO directly couples the current sources of the conventional LC VCOs through the back-gate instead of front-gate to generate quadrature signals. By the second harmonic injection locking, the two LC VCOs can generate quadrature signals without using on-chip transformer, or stability problem that is inherent in the direct front-gate second harmonic coupling. The proposed QVCO is implemented in $0.18{mu}m$ CMOS technology operating at 2 GHz with 5.0 mA core current consumption from 1.8 V power supply. The measured phase noise of the proposed QVCO is - 63 dBc/Hz at 10 kHz offset, -95 dBc/Hz at 100 kHz offset, and -116 dBc/Hz at 1 MHz offset from the 2 GHz output frequency, respectively. The calculated figure of merit(FOM) is about -174 dBc/Hz at 1 MHz offset. The measured image band rejection is 46 dB which corresponds to the phase error of $0.6^{circ}$.