The construction of implicit RKN is investigated in this paper. We finally obtain four four-stages implicit integrators by considering the symmetric, symplectic, and trigonometric fitting conditions. For the new obtained methods, we analyze their global convergence and stability property. And we carry out numerical experiments on some commonly considered problems in the literature. In view of the numerical experiments, we observe that the new methods outperform several efficient RKN methods in terms of accuracy and efficiency.