In this paper, we studied the contact angle behaviors on heterogeneous surfaces by a mean-filed free-energy lattice Boltzmann method recently proposed [Zhang et al., Phys. Rev. E, 69, 032602, 2004]. Simulation results showed that the Cassie law was valid when the heterogeneous patterns were smaller than or of the same order to the liquid-vapor interface thickness. A droplet would move spontaneously if it experienced unbalanced Young forces on a heterogeneous surface. Such self-movements were similar to previous experimental observations. Our simulations also showed more potential of the lattice Boltzmann method in future interfacial studies.