Distortion will exist in the range profile of the received radar stepped frequency signal of maneuvering target. To solve this problem, the integrated cubic phase function (ICPF) method is presented in this paper. First, the received signal is characterised as a three-order phase signal and performed with 1st-order differential operation. Next, ICPF of the processed back data is calculated to estimate and compensate the acceleration through dechirp operation. In addition, the estimation and compensation of the velocity of the residual signal are operated as well. Then the target's high resolution range profile can be obtained by IFFT. As the estimation of acceleration and velocity requires 1-D searching merely, the computational amount is quite small. Finally, the simulation is carried out in the situations of noiseless and low signal-to-noise ratio, and the test results prove the validity of this method in the paper.