A linear-correction least-squares(LCLS) estimation procedure is proposed for geolocation using frequency difference of arrival (FDOA) measurements only. We first analyze the measurements of FDOA, and further derive the Cramér-Rao lower bound (CRLB) of geolocation using FDOA measurements. For the localization model is a nonlinear least squares(LS) estimator with a nonlinear constrained, a linearizing method is used to convert the model to a linear least squares estimator with a nonlinear constrained. The Gauss-Newton iteration method is developed to conquer the source localization problem. From the analysis of solving Lagrange multiplier, the algorithm is a generalization of linear-correction least squares estimation procedure under the condition of geolocation using FDOA measurements only. The algorithm is compared with common least squares estimation. Comparisons of their estimation accuracy and the CRLB are made, and the proposed method attains the CRLB. Simulation results are included to corroborate the theoretical development. We first analyze the measurements of FDOA, and further derive the Cramera-Rao lower bound (CRLS) of geolocation using FDOA measurements. For the localization model is a nonlinear least squares (LS) estimator with a nonlinear constrained, a linearizing method is used to convert the model to a linear least squares estimator with a nonlinear constrained. The Gauss-Newton iteration method is developed to From the analysis of solving Lagrange multiplier, the algorithm is a generalization of linear-correction least squares estimation procedure under the condition of geolocation using FDOA measurements only. estimation accuracy and the CRLB are made, and the proposed method attains the CRLB. Simulation results are inclu ded to corroborate the theoretical development.