A novel class of k-space trajectories for magnetic resonance imaging (MRI) sampling using space-filling curves (SFCs) is presented here. More specifically, Peano, Hilbert and Sierpinski curves are used. We propose 1-shot and 4-shot variable density SFCs by utilizing the space coverage provided by SFCs in different iterations. The proposed trajectories are compared with state-of-the-art echo-planar imaging (EPI) trajectories for 128 × 128 and 256 × 256 phantom and brain images. The simulation results show that the readout time is reduced by up to 45% for the 128 × 128 image with little compromise in reconstruction quality. Also, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index are improved by 2.32 dB and 0.1009, respectively, with an 18% shorter readout time using the 4-shot Hilbert SFC trajectory for reconstructing a 256 × 256 brain MRI image.