Abstract: To improve the flexibility for the design of subdivision curves, a Laurent polynomial is constructed by means of its relationship with the generated polynomial of the subdivision scheme. The Laurent polynomial can generate a family of subdivision schemes with several parameters, which not only include some existing symmetric schemes, but also can be used to construct asymmetric schemes. The continuity and smoothness of the limit curve are analyzed for a five-point scheme with three parameters. Numerical examples are given to demonstrate the influence of parameters on the limit curves in some special cases and to show that sometimes the asymmetric subdivision has better approximating effect than symmetric one.