The intrinsic microwave surface impedance for a nearly ferroelectric superconducting film of finite thickness in the dielectric-like response is theoretically investigated. It is based on the electrodynamics of a nearly ferroelectric superconductor that incorporates the Maxwell's equations, the lattice equations for an ionic lattice, and the superconducting London equation as well. It is found that the surface resistance will be enhanced with decreasing the film thickness when the thickness is less than the London penetration depth. However it will begin to resonate as a function of film thickness at the thickness being more than one London penetration depth. The anomalous resonance peaks occur when the thickness equals the even multiple of the London penetration depth. In the frequency-dependent surface resistance, the number of the resonance peaks is strongly dependent on the film thickness, increasing with increasing the thickness. In addition, these peaks are not regularly spaced at a fixed interval. Discussion on this anomaly in the surface resistance will be given.