Using classical nucleation theory (CNT), a homogeneous condensation model has been developed in previous work to simulate condensation in a free expanding plume using the direct simulation Monte Carlo (DSMC) method. However, the accuracy of the CNT nucleation theory is questionable due to the unphysical assumptions such as the use of macroscopic cluster surface tension for small clusters and the lack of an incubation time for nucleation. In our earlier modeling of expanding flows we showed that the initial clusters, dimers, are created through the triple collision processes. Hence in this work we develop a kinetic nucleation model by generating stable dimers out of triple collisions. The new kinetic model will be implemented into a DSMC code and is used to simulate the cluster growth processes starting from dimers in a condensation plume. The distributions of cluster number density and size are compared for the simulations using the kinetic and CNT nucleation models.