Quadrature sampling has been widely applied in coherent radar systems to extract in-phase and quadrature (I and Q) components in the received radar signal. However, the sampling is inefficient because the received signal contains only a small number of significant target signals. This paper incorporates the compressive sampling (CS) theory into the design of the quadrature sampling system, and develops a quadrature compressive sampling (QuadCS) system to acquire the I and Q components with low sampling rate. The QuadCS system first randomly projects the received signal into a compressive bandpass signal and then utilizes the quadrature sampling to output compressive I and Q components. The compressive outputs are used to reconstruct the I and Q components. To understand the system performance, we establish the frequency domain representation of the QuadCS system. With the waveform-matched dictionary, we prove that the QuadCS system satisfies the restricted isometry property with overwhelming probability. For K target signals in the observation interval T, simulations show that the QuadCS requires just O(Klog(BT/K)) samples to stably reconstruct the signal, where B is the signal bandwidth. The reconstructed signal-to-noise ratio decreases by 3dB for every octave increase in the target number K and increases by 3dB for every octave increase in the compressive bandwidth. Theoretical analyses and simulations verify that the proposed QuadCS is a valid system to acquire the I and Q components in the received radar signals.