This study deals with a biologically inspired system called DNA Addition System (DAS). The system consists of four elements: a chain molecule; a set of free (elemental) molecules, all of which refer to the elements of DNA; a quasi-free molecule, which is the last elemental molecule of the chain molecule; and a molecular machine. When the system works, a definite reconfiguration, referred to as addition, takes place. Addition actually adds a free molecule to the chain molecule to make it grow longer. The molecular machine decides which type of free molecule should be added taking into account the informational state of the system. A simulation model is also developed based on DAS to help generate chain molecule applying successive additions. This model can be used to simulate chain molecules that exhibit the characteristics of genetic molecules (i.e. molecules with identifiable segments) and behaviors of dynamical systems. How to correlate the characteristics of a dynamical system with the characteristics of DAS is also pointed out. Further study should be carried out to enhance the knowledge of DAS from both theory and application points of view.