Many problems in real world, either natural or man-made, can be usefully represented by graphs or networks. Along with a complex topological structure, the weight is a vital factor in characterizing some properties of real networks. In this paper, we define a class of the weighted edge corona product networks. The generalized adjacency (resp., Laplacian and signless Laplacian) spectra with two different structures are determined. As applications, the number of spanning trees and Kirchhoff index of the weighted edge corona product networks are computed. •We first define a class of the weighted edge corona product networks.•Three types of spectra for that networks are given.•The number of spanning trees and Kirchhoff index of that networks are determined.