Image quality depends on the randomness of the k-space signal under-sampling in compressed sensing MRI (CS-MRI), especially for two-dimensional image acquisition. We investigate the feasibility of non-random signal under-sampling CS-MRI to stabilize the quality of reconstructed images and avoid arbitrariness in sampling point selection. Regular signal under-sampling for the phase-encoding direction is adopted, in which sampling points are chosen at equal intervals for the phase-encoding direction while varying the sampling density. Curvelet transform was adopted to remove the aliasing artifacts due to regular signal under-sampling. To increase the incoherence between the measurement matrix and the sparsifying transform function, the scale of the curvelet transform was varied in each iterative image reconstruction step. We evaluated the obtained images by the peak-signal-to-noise ratio and root mean squared error in localized 3×3 pixel regions. Simulation studies and experiments showed that the signal-to-noise ratio and the structural similarity index of reconstructed images were comparable to standard random under-sampling CS. This study demonstrated the feasibility of non-random under-sampling based CS by using the multi-scale curvelet transform as a sparsifying transform function. The technique may help to stabilize the obtained image quality in CS-MRI.