By studying the structural characteristics of linear crossed polyomino chain X_n and crossed polyomino cylinder chain G_n, the Laplacian spectra of X_n and G_n are calculated by the Laplacian eigenvalues of the composite graph, and the analytic expressions of Kirchhoff index, degree-Kirchhoff index and the number of spanning trees of X_n and G_n are derived. And we show that when n tends to be infinity, the Kirchhoff index of crossed polyomino cylinder chain G_n is one-half of the Kirchhoff index of the linear crossed polyomino chain X_n.