Zircaloy fuel cladding is the first pressure boundary of a nuclear power plant, the reliability of which is crucial to maintaining the nuclear safety. Since the oxide film accumulated on the cladding surface decreases the thermal conductivity and accelerates the corrosion rate of the fuel rods, it is essential to accurately assess the oxide film thickness. Eddy current testing (ECT) is the predominant technology for measuring oxide film thickness in pool-side inspections. By far, ECT requires pre-calibration, which requires expensive calibration samples and is time-consuming. This article presents a novel ECT technology with stacked array coils that are separated by the insulation layers with a thickness of tens of microns. These coils are excited successively in chronological order and the induced voltages are recorded each time, resulting in a data matrix. The distances of coils serve as the interior thickness standard. A data processing procedure is developed to calculate the oxide film thickness from the matrix without the necessary of pre-calibration. An adaptive weight algorithm is proposed to reduce errors of the calculated thickness. The maximum absolute measurement error is under$4.5~\mu $m, while the weight correction reduces the maximum error to$3.74~\mu $m. Compared with existing calibration methods, this method appears to streamline the calibration procedure without significantly compromising measurement accuracy.