The equilibrium strategy is considered for a continuous-time newsvendor problem with the return policy and shortage cost. In the continuous-time newsvendor problem, the supplier and the retailer want to find the optimal strategy to maximize the expected terminal profit. An optimization problem is studied which is a continuous-time newsvendor problem with return policy and shortage cost. By using the principle of stochastic maximum, the existence and uniqueness of the equilibrium strategy are proved for this optimization problem and the conditions are obtained, which assure the equilibrium strategy. When the retail price is exogenous, the combined effect of the return policy and the shortage cost are proved to increase a lot the optimal order quantity of the retailer and the optimal whole sale price of the supplier. The numerical analysis shows the sensitive about the optimal wholesale price and the optimal order strategy.