This paper presents some convergence analysis of a new distributed algorithm, which is inspired by the celebrated BP (Belief Propagation) algorithm, for networked estimation in large-scale sparse systems. The proposed algorithm owns fast convergence rate and other advanced properties of the BP algorithm. We reveal that the distributed algorithm is guaranteed to converge correctly under the assumption that the system is generalized diagonally dominant. The convergence analysis for both acyclic graphs and loopy graphs have been studied. Specifically, the distributed algorithm will converge after finite number of iterations, which is equal to the diameter of the network graph, if the graph is acyclic. For a loopy network, the distributed algorithm is guaranteed to converge to the optimal estimates asymptotically. It can be shown from simulation results that the proposed distributed algorithm outperforms some existing distributed estimation algorithms.