The Total Variation (TV) method is often used to reconstruct the Compressed Sensing Magnetic Resonance Imaging (CS-MRI), however, it can generate the "stair effect” in the reconstructed MR image. In this paper, there types of TV extension based methods, i.e. High Degree Total Variation (HDTV), Total Generalize Variation (TGV) and Group-Sparsity Total Variation (GSTV), are proposed to implement the sparse reconstruction of MR image. In addition, the shift-invariant discrete wavelet transform are integrated into these TV extension based methods as the sparsifying transform. The Fast Composite Splitting Algorithm (FCSA) is adopted to solve the convex optimization problem of CS-MRI reconstruction. And the Two different types of MR images with radial sampling trajectory are used to validate the reconstruction performance of CS-MRI by using the TV extension methods. The experiment results show that the TV extension based models can overcome the shortcomings of TV based model. Moreover, compared with HDTV and TGV methods, the GSTV method can obviously improve the reconstruction quality with higher Signal-to-Noise Ratio (SNR).