A hybrid cover for use in the construction of a pet bed that may make use of a used pillow for a cushioning member in conjunction with the hybrid cover in constructing the pet bed. The hybrid cover includes a bed portion and a flap portion that may be disposed in an overlapping and non-overlapping position with respect to the bed portion. A pillow may be provided in an interior space of the bed portion. The pillow may have a scent that is smellable at an exterior of the hybrid cover when a pet bed is constructed using the hybrid cover and the pillow.
