Abstract: A fast method for joint estimation of the time-frequency offset for linear frequency modulated signals based on the Radon-Ambiguity transform (RAT) is proposed in this paper. According to peak positions of the RAT of a LFM signal on different angles, a set of equations with the time-frequency offset as the unknowns can be established and the time-frequency offset can be estimated by solving the equations. For signals disturbed by noise, errors of the RAT will cause the equations having no solutions. In order to eliminate the noise, the least square method is used to estimate the time-frequency offset. Because the proposed algorithm does not need to calculate the value of each point on the 2-D Ambiguity plane and the RAT for sampled signals can be realized rapidly by several processes of the fast Fourier transform, the proposed method has advantage of low computational cost. Simulation results show that the proposed algorithm can ensure the accuracy of the estimation of the time-frequency offset as well as is computationally efficient compared with common methods based on peak searching of the Ambiguity function.