We propose a sparsity-based approach to track multiple targets in a region of interest using an orthogonal-frequency-division multiplexing (OFDM) radar. We observe that in a particular pulse interval the targets lie at a few points on the delay-Doppler plane and hence we exploit that inherent sparsity to develop a tracking procedure. The use of an OFDM signal not only increases the frequency diversity of our system, as different scattering centers of a target resonate variably at different frequencies, but also decreases the block-coherence measure of the equivalent sparse measurement model. In the tracking filter, we exploit this block-sparsity property in developing a block version of the compressive sampling matching pursuit (CoSaMP) algorithm. We present numerical examples to show the performance of our sparsity-based tracking approach and compare it with a particle filter (PF) based tracking procedure. The sparsity-based tracking algorithm takes much less computational time and provides equivalent and sometimes better, tracking performance than the PF-based tracking.