Modern positron emission tomography (PET) detectors are made from pixelated scintillation crystal arrays and readout by Anger logic. The interaction position of the gamma-ray should be assigned to a crystal using a crystal position map or look-up table. Crystal identification is a critical procedure for pixelated PET systems. In this paper, we propose a novel crystal identification method for a dual-layer-offset LYSO based animal PET system via Lu-176 background radiation and mean shift algorithm. Single photon event data of the Lu-176 background radiation are acquired in list-mode for 3 h to generate a single photon flood map (SPFM). Coincidence events are obtained from the same data using time information to generate a coincidence flood map (CFM). The CFM is used to identify the peaks of the inner layer using the mean shift algorithm. The response of the inner layer is deducted from the SPFM by subtracting CFM. Then, the peaks of the outer layer are also identified using the mean shift algorithm. The automatically identified peaks are manually inspected by a graphical user interface program. Finally, a crystal position map is generated using a distance criterion based on these peaks. The proposed method is verified on the animal PET system with 48 detector blocks on a laptop with an Intel i7-5500U processor. The total runtime for whole system peak identification is 67.9 s. Results show that the automatic crystal identification has 99.98% and 99.09% accuracy for the peaks of the inner and outer layers of the whole system respectively. In conclusion, the proposed method is suitable for the dual-layer-offset lutetium based PET system to perform crystal identification instead of external radiation sources.