An endoscopic fluorescence imaging system based on fiber speckle illumination is proposed. In this system, a multimode fiber for transmission of excitation laser light and collection of fluorescence is inserted into a conventional flexible endoscope. Since the excitation laser light has random speckle structure, one can detect fluorescence signal corresponding to the irradiation pattern if the sample contains fluorophores. The irradiation pattern can be captured by the endoscope camera when the excitation wavelength is within the sensitivity range of the camera. By performing multiple measurements while changing the irradiation pattern, a fluorescence image is reconstructed by solving a norm minimization problem. The principle of our method was experimentally demonstrated. A 2048 pixels image of quantum dots coated on a frosted glass was successfully reconstructed by 32 measurements. We also confirmed that our method can be applied on biological tissues.