A computationally efficient time delay and Doppler estimation algorithm is proposed for active sonar with a Linear Frequency Modulated (LFM) signal. To reduce the computational burden of the conventional estimation algorithm, an algebraic equation is used which represents the relationship between the time delay and the Doppler in the cross-ambiguity function (CAF) of the LFM signal. The algebraic equation is derived based on the Fast Maximum Likelihood (FML) algorithm. The use of this algebraic relation enables the time delay and Doppler to be estimated with two 1-D searches instead of the conventional 2-D search.