Abstract: The nuclear low-lying excitation spectra are very important for understanding nuclear structure. The excitation energies of 2_1^+ and 4_1^+ states are systematically studied by using the multi-task Back Propagation(BP) neural network method. The BP neural network can well fit the low-lying excitation energies in a large energy range from about 0.1 MeV to about several MeV, by including a physical quantity related to nuclear collectivity on input layer besides proton and neutron numbers. Compared with the five-dimensional Collective Hamiltonian(5DCH) method, BP neural network can better reproduce the isotope trend of low excitation energy of nuclei, including the rapid increase of low excitation energy of magic nuclei caused by shell effect. The prediction accuracy for 2_1^+ and 4_1^+ states is improved by about 80% and 75%, respectively, which are similar to those of single-task neural network, while the learning ability for low excitation spectra in light and neutron-deficient nuclei is improved, indicating that multi-task neural network can achieve a unified and precise calculation of multiple excitation energies.