In the present paper we demonstrate that there exists a new type of neutron stars in the tensor-multi-scalar theories of gravity. We call this new type of neutron stars topological neutron stars. In addition to the standard characteristics of the usual neutron stars the topological neutron stars are also characterized by a topological charge. We numerically construct explicit examples of topological neutron stars in tensor-multi-scalar theories whose target space is S3. Besides the topological charge the topological neutron stars also exhibit other attractive features which can place them among the realistic compact objects that could exist in nature. For example they possess zero scalar charge and thus evade the strong binary pulsar constraints on the dipole scalar radiation.