This paper presents an algorithm for estimating the parameters of multicomponent cubic phase signals. This algorithm combines the product generalized cubic phase function (PGCPF) and the product cubic phase function (PCPF) which are used to estimate the cubic phase coefficient and chirp rate of the cubic phase signal, respectively. This algorithm starts by estimating the parameters of the signal component with the strongest amplitude. Then removing the signal component whose parameters have been estimated, it proceeds to estimate the next signal component, and so on, until all of the signal components have been estimated. Numerical simulations are carried out to validate the performance of the proposed algorithm.