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Compressed sensing (CS) and parallel imaging (PI) have been widely studied for accelerating MRI reconstruction. Furthermore, the serial combination methods of CS and PI have been proposed for even higher speed of reconstruction. However, both reconstructed signals by CS and PI are not as accurate as acquired MR signals, so that errors of CS reconstruction as the first step will be propagated and even amplified to deteriorate PI reconstruction quality in the second step. Based on our previous work - nonlinear GRAPPA (NLGRAPPA), we proposed a novel serial combination of CS and NLGRAPPA (CS-NLGRAPPA) reconstruction. The generalized kernel regression model of NLGRAPPA can remove error effects of inaccurate signal reconstruction by CS. Experimental results using phantom and in vivo data demonstrate that the proposed CS-NLGRAPPA method can significantly improve the reconstruction quality over the existing method and push net reduction factor around 4.