As one of the most important subsystems in cities, urban street networks have recently been well studied by using the approach of complex networks. This paper proposes a growing model for self-organized urban street networks. The model involves a competition among new centers with different values of attraction radius and a local optimal principle of both geometrical and topological factors. We find that with the model growth, the local optimization in the connection process and appropriate probability for the loop construction well reflect the evolution strategy in real-world cities. Moreover, different values of attraction radius in centers competition process lead to morphological change in patterns including urban network, polycentric and monocentric structures. The model succeeds in reproducing a large diversity of road network patterns by varying parameters. The similarity between the properties of our model and empirical results implies that a simple universal growth mechanism exists in self-organized cities.