Polymer crystallization is the most important part in determining the performance of polymeric materials. The twin-lattice model originally provided by Lennard-Jones and Devonshire, developed by Pople and Karasz and other researchers, is extended for describing the thermodynamics of polymer crystallization. The positional order of segments and the orientational order of bonds are considered in this model. The free energy of polymers is obtained by further introducing the conformational energy and entropy, and thus a new parameter is defined, which is the ratio of conformational energy and positional diffusion energy. We studied two kinds of processes in polymer crystallization, including the process with plastic crystal phase and without any mesophases. The choice of crystallizing process is determined by the magnitude of lattice energy and conformational energy. The solid-solid transition from crystal to plastic crystal shows a significant dependence on the conformational energy. Considering data reliability, n-paraffins are chosen as the representation of polymers to compare the predictions of the model with experimental observations. We predict the number of carbons beyond which the rotator phase disappears, which is quite in agreement with the experiments. These calculations and results show this model can provide a new understanding to the crystallization of polymers.