We propose a scheme for simulating the dynamics of neutrino oscillations using trapped ions. For neutrinos in 1 + 1 dimensions, our scheme is experimentally implementable with existing trapped-ion technology. We show that the three-generation neutrino oscillations can be realized with three ions for 1 + 3 and 1 + 1 dimensions where the latter case only requires experimentally proven two-ion interactions. For this case, we discuss two setups utilizing different types of spin-spin interactions. Our method can be readily applied to two-generation neutrino oscillations requiring fewer ions and lasers. We give a brief outline of a possible experimental scenario.