Inventory management of deteriorating drugs has attracted considerable attention recently in hospitals. Drugs are a kind of special product. Two characteristics of some drugs are the shorter shelf life and high service level. This causes hospitals a great deal of difficulty in inventory management of perishable drugs. On one hand, hospitals should increase the drug inventory to achieve a higher service level. On the other hand, hospitals should decrease the drug inventory because of the short shelf life of drugs. An effective management of pharmaceuticals is required to ensure 100% product availability at the right time, at the right cost, in good conditions to the right customers. This requires a trade-off between shelf-life and service level. In addition, many uncontrollable factors can lead to random lead time of drugs. This paper focuses on deteriorating drugs with stochastic lead time. We have established a stochastic lead time inventory model for deteriorating drugs with fixed demand. The lead time obeyed a certain distribution function and shortages were allowed. This model also considered constraints on service level, stock space and drug shelf life. Through the analysis of the model, the shelf life of drugs and service level were weighted in different lead time distributions. Empirical analysis and sensitivity analysis were given to get reach important conclusions and enlightenment.