Fuel assemblies, serving as the heat-releasing components within nuclear reactors, constitute the energy source for nuclear power generation. Among these, the zirconium-based cladding of nuclear fuel acts as the primary safety barrier in nuclear power plants. It effectively prevents the dispersion of fission products while conducting heat away, thereby avoiding fuel corrosion due to cooling. Therefore, the structural characteristics of cladding tubes are closely related to the performance of fuel assemblies. Conducting effective non-destructive testing on zirconium-based fuel cladding to achieve high-precision wall thickness and electrical conductivity characterization remains a critical challenge in nuclear safety inspection. This article investigates a novel stacked eddy current sensor for the conductivity and thickness measurement of a cladding tube. Firstly of all, a stacked array eddy current sensor consisting of three absolute coils is designed. Based on the structural configuration of this sensor, the analytical solution is established for cladding tube detection. Based on the analytical solution, the s cross-frequency of self-inductance can be extracted in sweep mode. Moreover, the logarithm of the cross-frequency exhibits a linear relationship with the lift-off distance. The slope of this linear relationship depends solely on the wall thickness and is independent of the conductivity of the material. Consequently, the wall thickness can be estimated by the slope of the fitting line. Subsequently, the eddy current testing problem can be transformed into a least-squares problem for the cladding tube. Taking the wall thickness measurement results as prior information, the conductivity of the cladding tube is inverted through the improved Newton iteration algorithm. Finally, the eddy current testing experiment platform is established to validate the effectiveness of the proposed method, and the results show that the maximum measurement error of the proposed method is only 1.3%.