The preparation of non-trivial states is crucial to the study of quantum many-body physics. Such states can be prepared with adiabatic quantum algorithms, which are restricted by the minimum spectral gap along the path. In this letter, we propose an efficient method to adiabatically prepare tensor networks states (TNSs). We maximize the spectral gap leveraging degrees of freedom in the parent Hamiltonian construction. We demonstrate this efficient adiabatic algorithm for preparing TNS, through examples of random TNS in one dimension, AKLT, and GHZ states. The Hamiltonian optimization applies to both injective and non-injective tensors, in the latter case by exploiting symmetries present in the tensors.