The paper considers the design of frequency diverse array (FDA) for co-located multi-input multi-output (MIMO) radar employing a joint grid-free direction of arrival (DOA) and range estimation method, and proposes a design approach using a nested array as the physical antenna array. Specifically, an inner uniform linear subarray of the nested array is employed for the transmitting array, while the entire nested array serves as the receiving array. Moreover, a grid-free method using atomic norm minimization (ANM) is employed to realize joint DOA and range estimation, making full use of the extended virtual array aperture by the nested array. One of key features of the proposed nested FDA MIMO radar is that it enables fine-tuning of the balance between the DOA and range estimation performance by adjusting the level of the nested array. The numerical results validate the effectiveness of the proposed approach, highlighting the feasibility of controlling the balance between the DOA and range estimation performance by adjusting the level of the nested array. Moreover, the proposed nested FDA MIMO radar outperforms the FDA MIMO radar with a uniform linear array (ULA) in terms of both DOA and range estimation performance for the appropriate choice of the level.