In this paper, a budget constrained dynamic (multi-period) uncapacitated facility location-network design problem (DUFLNDP) is investigated. The facility location-network design problem deals with the determination of the optimal locations of facilities and the design of the underlying network simultaneously. The objective is to minimize the total travel costs for customers and operating costs for facilities and network links subject to a constraint on the budget for opening and/or closing facilities and constructing links. We propose a mixed- integer non-linear programming model that considers a dynamic planning horizon in facility location-network design problem. An efficient hybrid algorithm based on simulated annealing algorithm and exact methods to solve the proposed model is also presented. Finally, the performance of our proposed algorithm is tested on extensive randomly generated instances and also compared with CPLEX solver