In recent years, it has been pointed out that the maximum accelerating gradient of a superconducting RF cavity can be increased by coating the inner surface of the cavity with a multilayer thin-film structure consisting of alternating insulating and superconducting layers. In this structure, the principal parameter that limits the performance of the cavity is the critical magnetic field or effective Hc1 at which vortices begin penetrating into the superconductor layer. This is predicted to depend on the combination of the film thickness. We made samples that have a NbN/SiO₂ thin-film structure on a pure Nb substrate with several layers of NbN film deposited using DC magnetron sputtering method. Here, we report the measurement results of effective Hc1 of NbN/SiO₂(30 nm)/Nb multilayer samples with thicknesses of NbN layers in the range from 50 nm to 800 nm by using the third-harmonic voltage method. Experimental results show that an optimum thickness exists, which increases the effective Hc1 by 23.8 %.