The response of a graphene-based humidity sensor is considered as a function of film structures. Analysis of the resistance changes due to water molecule adsorption on the graphene or multi-layer graphene (MLG) surface is performed for films with different structures and resistivities from hundreds of ohms/sq to hundreds of kilo-ohms/sq. The results revealed possible increase, decrease and non-monotonous behavior of resistance with changes in film structure. Adsorption of water molecules at grain boundary defects is assumed to lead to an increase in film resistivity due to the donor property of water and the p-type conductivity of graphene. Another type of conductive center with a higher capture cross-section is realized in the case of water molecule adsorption at edge defects in MLG films (the formation of conductive chains with ionic conductivity). If these chains form a continuous network the film resistivity decreases. The result of the competition between the opposite effects of the conductivity compensation and formation of the water-based conductive chains depends on the film structure and determines the response of humidity sensors. Sensor sensitivity is found to increase when only one type of defect determines water adsorption (edge defects or grain boundary defects).