To accurately identify the range of each target, traditional Multiple-Input Multiple-Output (MIMO) radar techniques not only require designing a shift matrix to describe different range bins but also a large number of snapshots. To alleviate this problem, a multidimensional parameter estimation method based on sparse iteration is proposed for a MIMO radar with Frequency Diverse Array (FDA). The FDA-MIMO radar uses small frequency increments across the array elements, and its transmit steering vector is a function of both range and angle. On the basis of the feature of the FDA-MIMO radar, we consider a weighted lq (0<q ≤1) minimization problem that is solved using a sparse iterative algorithm. Finally, the target parameters (the amplitude, range, and angle) are obtained using a single snapshot. Moreover, numerical simulations are used to demonstrate the superior performance of the proposed method compared with those of DAS, IAA, and IAA-R.