The first excited 2(+) energy states of nuclei give much substantial information related to the nuclear structure. All excited states of nuclei are shown regularities in spin, parity, and energy, including these levels. In the even-even nuclei, the first excited state is generally 2(+), and the energy values of them increase as the closed shells are approached. The nuclei's excited levels can be investigated using theoretical nuclear models, such as the nuclear shell model. In the present study, we have used artificial neural networks to determine the energies of the first 2(+) states in the even-even nuclei in the nuclidic chart as a function of Z and N numbers for the first time. According to the results, the method is convenient for this goal. One can confidently use the method for predicting the first 2(+) state energy values whose experimental values do not exist in the literature.