The inventory routing problem (IRP) is studying how to deliver products to several customers from the supplier, which is a combination of inventory management and vehicle routing problems. This paper studied an IRP with considering the time consumption in transportation, which is the replenishment lead time. In this problem, the delivery sequence impacts the transport cost and the replenishment lead time of customers. Three decisions should be made: 1) which customer should be replenished; 2) how much goods should be delivered; 3) the delivery sequence. In this paper, we proposed a single period model, which can very easily be extended to a rolling horizon policy for solving the infinity horizon IRP. We discussed the closed-form solution of robust inventory policy and proposed a Genetic Algorithm to solve this problem. Finally, a numerical example is provided to indicate the feasibility of the algorithm.