In this article, an analysis of nonlinear three-dimensional (3-D) morphological instabilities in chemical vapor deposition (CVD) is presented. We establish a set of mathematically governing equation and boundary condition for the system of CVD and derive a weakly nonlinear evolution equation by considering a diffusion-limited growth condition to study the morphological instabilities in the CVD process. This evolution equation not only can predict the behaviors of interfacial growth of films, but can also be a basis of weakly nonlinear analysis. The analysis from critical condition is adopted to investigate the two-dimensional (2-D) band-like cells and the 3-D hexagonal structures.