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This paper delves into the problem of direct position determination (DPD) for non-Gaussian sources. Existing DPD algorithms are hindered by their high computational complexity from exhaustive grid searches and a disregard for the received signal characteristics by multiple nested arrays (MNAs). To address these issues, the paper proposes a novel DPD algorithm for non-Gaussian sources with MNAs: the Discrete Fourier Transform (DFT) and Taylor compensation algorithm. Initially, the fourth-order cumulant matrix of the received signal is computed, and the vectorizing method is applied. Subsequently, a computationally efficient DPD cost function is proposed by leveraging a normalized DFT matrix to reduce complexity. Finally, first-order Taylor compensation is utilized to enhance the accuracy of the localization results. The superiority of the proposed algorithm is demonstrated through numerical simulation results.