Direct position determination (DPD) approaches of non-circular (NC) signals for distributed antenna arrays are outstanding in location accuracy and available degrees of freedom. Nevertheless, the existing grid-based DPD approaches involve unnecessary computational costs because of NC phases. Besides, the cost function utilized in DPD could cause performance deterioration as ignoring the non-homogeneity error of the received data. To this end, we propose a DPD approach implemented by polynomial rooting and optimal weighting. Aiming to reduce computational costs, we first construct a computationally efficient cost function. Meanwhile, to mitigate the adverse impact induced by non-homogeneity errors in an effective manner, we assign an optimal weight to each antenna array. Simulation results demonstrate that the proposed approach achieves a good compromise between performance and computational complexity.