This research takes into account the variable lead time and stochastic demand for inventory. First, we collected demand and lead time data to test their goodness of fit, then, based on the verified distributions of demand and lead time to build up a multi-variate inventory management model. We applied the optimal technique and numerical calculation method to search for the optimal ordering quantity and reorder point to obtain the minimum total expected cost of inventory. Furthermore, according to the optimal reorder point, we found out the optimal service rate about its corresponding inventory.