Both Parallel Imaging (PI) and Compressed Sensing (CS) can significantly accelerate the MRI acquisition process. Moreover, in the context of CS, it has been recently shown that the reconstruction quality can be drastically enhanced by a “Spread Spectrum (SS) technique” using quadratic phase profiles in MRI, which amounts to the modulation of the image probed by a linear chirp. Combination of CS and PI for higher accelerations is of great interest. In this work, we propose Parallel Spread Spectrum MR Imaging (PSSI) as a generalization of SS technique for parallel MRI. Extensive numerical simulations on the Shepp-Logan phantom together with some illustrations on real brain images demonstrate that the SS can be used as a complement of parallel imaging for higher accelerations, whilst applying this technique in parallel MRI can also drastically enhance the reconstruction quality and stability rather than CS using basic Fourier measurements.