Quadrature sampling is an effective technique for extracting digital in-phase and quadrature (I/Q) components in the modulated radio signals. Existing quadrature sampling techniques require the sampling rate to be at least twice of the bandwidth of the bandpass signal. The newly introduced compressive sampling theory makes sampling the analog signal at a low sampling rate possible if the signal has a sparse representation. This paper merges the two sampling techniques and develops a quadrature compressive sampling (QuadCS) system to obtain the digital I/Q components with low-rate samplers. The operation principle of the QuadCS system is described and the formulation to recover the I/Q components from the low-rate samples is developed. The simulation results demonstrate that the QuadCS is effective for acquiring and reconstructing the I/Q components sparse in waveform-matched dictionary. With the QuadCS system, the simulated signals can be sampled at about 10% Nyquist sampling rates. In addition, the output signal-to-noise ratio is improved about 15–20dB.