This study establishes a discrete-time inventory model with a smoothing procurement strategy in dual sourcing. Specifically, an assembly manufacturer purchases components from two suppliers: one overseas supplier with a long lead time but a low price, and one local supplier with a short lead time but a high price. A smoothing procurement approach taking into account previous ordering record and current demand is adopted by the assembly manufacturer. We start by exploring the scenario where storage space is not a constraint. The cost-minimization conditions for single sourcing and dual sourcing are studied. Assuming demand follows a normal distribution, the optimal order quantities and inventory levels are subsequently derived and shown to follow the same distribution. By comparing the inventory costs, it is found that dual sourcing is superior to single sourcing. Then, we examine the scenario where an assembly manufacturer with limited storage space collaborates with a third-party logistics company. The optimal order quantities, inventory levels, smoothing procurement coefficient and storage space are derived for the assembly manufacturer. Finally, numerical experiments with practical data are constructed to verify our findings.