In this paper, we study a unified model of dark matter and dark energy obtained from Dirac–Born–Infeld (DBI) action in string theory. Two accelerated expansions in universe can be unified in this action. By using the Markov Chain Monte Carlo method, we fit the current observational data to constrain the model parameters in this unified model, where various density parameters as model parameters are included, and their constraint values are: , , and . In addition, the Hubble constant and cosmic age are and (Gyr), respectively. According to the constraint results on model parameters we discuss the evolutions of some cosmological quantities in structure formation, such as the density contrast and the growth variable. At last, the evolution of geometrical quantity is studied to distinguish the unified models of dark sectors with the cosmological constant model. It is shown that this unified model of dark matter and dark energy is attractive to interpret the accelerating universe.