1. A fluorescence endoscope apparatus comprising: an illuminating portion that radiates excitation light and illumination light onto an imaging subject; a fluorescence imaging portion that acquires a fluorescence image by capturing fluorescence emitted at the imaging subject due to the irradiation with the excitation light from the illuminating portion; a storage portion that stores the fluorescence image acquired by the fluorescence imaging portion; a return-light imaging portion that acquires a return-light image by capturing return light returning from the imaging subject due to the irradiation with the illumination light from the illuminating portion; an image-information extracting portion that extracts, from the return-light image acquired by the return-light imaging portion, image information that expresses the intensity of the illumination light radiated onto the imaging subject; a number-of-integrated-images setting portion that sets a number of integrated images so that the number is decreased with an increase in the intensity of the illumination light, based on the image information extracted by the image-information extracting portion; and an average-image generating portion that generates an average image by averaging the fluorescence images, stored in the storage portion, in a number corresponding to the number of integrated images set by the number-of-integrated-images setting portion.