Segmentation of fundamental heart sounds-S1 and S2 is important for automated monitoring of cardiac activity including diagnosis of the heart diseases. This paper proposes a novel hybrid method for S1 and S2 heart sound segmentation using group sparsity denoising and variation mode decomposition (VMD) technique. In the proposed method, the measured phonocardiogram (PCG) signals are denoised using group sparsity algorithm by exploiting the group sparse (GS) property of PCG signals. The denoised GS-PCG signals are then decomposed into subsequent modes with specific spectral characteristics using VMD algorithm. The appropriate mode for further processing is selected based on mode central frequencies and mode energy. It is then followed by the extraction of Hilbert envelope (HEnv) and a thresholding on the selected mode to segment S1 and S2 heart sounds. The performance advantage of the proposed method is verified using PCG signals from benchmark databases namely eGeneralMedical, Littmann, Washington, and Michigan. The proposed hybrid algorithm has achieved a sensitivity of 100%, positive predictivity of 98%, accuracy of 98% and detection error rate of 1.5%. The promising results obtained suggest that proposed approach can be considered for automated heart sound segmentation.