This paper investigated a Subsample Time delay Estimation (STE) algorithm based on the amplitude of cross-correlation function to improve the estimation accuracy. In this paper, a rough time delay estimation is applied based on traditional cross correlator, and a fine estimation is achieved by approximating the sampled cross-correlation sequence to the amplitude of the theoretical cross-correlation function for linear frequency modulation (LFM) signal. Simulation results show that the proposed algorithm outperforms existing methods and can effectively improve time delay estimation accuracy with the complexity comparable to the traditional cross-correlation method. The theoretical Cramér-Rao Bound (CRB) is derived, and simulations demonstrate that the performance of STE can approach the boundary. Eventually, four important parameters discussed in the simulation to explore the impact on Mean Squared Error (MSE).