Magnetic Resonance Imaging (MRI) is an essential medical imaging tool limited by the data acquisition speed. Compressed Sensing is a newly proposed technique applied in MRI for fast imaging with the prior knowledge that the signals are sparse in a special mathematic basis (called the 'sparsity' basis). During the exploitation of the sparsity in MR images, there are two kinds of 'sparsifying' transforms: predefined transforms and data adaptive transforms. Conventionally, predefined transforms, such as the discrete cosine transform and discrete wavelet transform, have been adopted in compressed sensing MRI. Because of their independence from the object images, the conventional transforms can only provide ideal sparse representations for limited types of MR images. To overcome this limitation, this work proposed Singular Value Decomposition as a data-adaptive sparsity basis for compressed sensing MRI that can potentially sparsify a broader range of MRI images. The proposed method was evaluated by a comparison with other commonly used predefined sparsifying transformations. The comparison shows that the proposed method could give a sparser representation for a broader range of MR images and could improve the image quality, thus providing a simple and effective alternative solution for the application of compressed sensing in MRI.