Abstract: Cubic phase signal is always used to model the radar echoes from complex moving targets, but it contains a lot of unknown parameters and has much difficulty in its parameter estimation. Motivated by this, a method contains two sub-steps is present in this paper to estimate the parameters of cubic phase signals. Firstly, the Radon transform is used to extract the straight line which corresponding to a cubic phase component after doing cubic phase transform for signal, thereby, the initial value of the phase parameters can be obtained. Then, the simplex method is utilized to optimize the maximum likelihood estimation function to get the accuracy estimating results and the initial value can be used to initialize the optimization process. The procedures for single-component and multi-components cubic phase signal parameters estimation are presented. Simulation results showed that the algorithm can works at a low signal to noise ratio threshold and reaches the CRB.