Abstract: The direct positioning(DP) problem of off-grid quadrature amplitude modulation (QAM) signals is deeply studied in this paper. Existing DP algorithms are limited by high computational complexity and off-grid modeling error. In order to solve these problems, a DP algorithm for off-grid QAM signals based on Taylor compensation is proposed in the paper. Firstly, Gaussian noise is suppressed by fully leveraging the characteristics of receiving QAM signals with multi-nested arrays and the antenna aperture is expanded at the same time, thereby increasing the available degrees-of-freedom. Secondly, a DP cost function with high computational efficiency is constructed by means of discrete Fourier transform method, so as to reduce the high computational complexity induced by exhaustive grid search. Finally, the bias of position estimation is calculated using the first Taylor series expansion technique and then compensated for improving positioning accuracy. Numerical simulation results show that the proposed algorithm out-performs the traditional DP algorithm based on spatially-smoothed subspace data fusion and Capon DP algorithm in terms of positioning accuracy, while maintaining lower computational complexity.