Given a simple connected graph G, we consider two iterated constructions associated with G: F^k (G) and R^k (G) . In this paper, we completely obtain the normalized Laplacian spectrum of F^k (G) and R^k (G) , with k ≥2, respectively. As applications, we derive the closed-formula of the multiplicative degree-Kirchhoff index, the Kemeny’s constant, and the number of spanning trees of F^k (G)  , R^k (G) , r-iterative graph ,F_r^k (G)  and r-iterative graph , where k ≥2 and r ≥1 . Our results extend those main results proposed by Pan et al. (2018), and we provide a method to characterize the normalized Laplacian spectrum of iteratively constructed complex graphs.