Compressed Sensing (CS) technique is used in MRI to reconstruct images from randomly undersampled k-space. Since the samples in the center of k-space have more energy than that of periphery, the random undersampling should have been variable density over k-space. In this paper, we have presented a sampling scheme to achieve variable density undersampling in CS-MRI. It is based on a probability density function whose sampling density scaling varies according to a power of distance from the origin. The density values around the origin (a small radial distance) are forced to one such that no higher energy sample around origin of k-space is missed out. The sampling scheme is applied on the k-space samples of fully acquired brain MR image. To comply with practical requirements, the sampling is done only along the phase encode direction. Image is reconstructed from the undersampled data using non-linear reconstruction method. Analysis is done based on the reconstruction quality to empirically determine the radial distance (where all the samples are acquired) and to study the reconstruction performance under various undersampling factors (0.3, 0.4 and 0.5). The value of optimum radial distance obtained is 0.125. For the undersampling factor of 0.4 (2.5 times acceleration in data acquisition), a faithful reconstruction is achieved with the PSNR of 33 dB.