The vanadium dioxide (VO2) thin film, usually employed as an infrared detector, exhibits hysteresis in its resistance-temperature characteristic. Considering a polycrystalline VO2 thin film as a composite medium, containing semiconducting and metallic microcrystals, the well-known effective-medium approximation theory is employed to relate the volume fraction of the semiconducting microcrystals to the effective film resistance. A phenomenological model is first proposed for describing the hysteretic dependence of volume fraction on temperature. From this, a model for hysteresis in the resistance-temperature characteristic is then derived, and a procedure for estimating the model parameters is outlined. The model reproduces the more important hysteretic characteristics such as the major, minor, and nested loops, in good agreement with the experimental characteristics.