A two-dimensional lattice Boltzmann model is constructed to simulate the evaporation of a single droplet on a homogenous wetting substrate. An evaporation model is used in the simulation to describe the mass loss from the surface of the evaporating droplet. In addition, a partial wetting boundary condition is imposed on the lattice sites on the substrate surface to determine the wettability of the substrate. The evaporation of a single droplet in ambient vapor shows a linear decrease in the square of the droplet radius, which agrees well with the d(2) law for an evaporating droplet. During the evaporation of a droplet on a hydrophobic substrate, the wetting diameter decreases while the contact angle remains constant. During the evaporation of a droplet on a hydrophilic substrate, the wetting diameter decreases while the contact angle remains almost constant when a partial wetting boundary condition is imposed. However, three stages of contact line motion are observed when the partial wetting boundary condition is modified to describe the dynamical change in the contact angle, and this observation agrees well with a previous study by other investigtors. In addition, internal fluid flows towards the contact line of the droplet in the pinning stage of the evaporation are discussed.