This paper investigates the cost-profit sharing contract for a closed-loop supply chain(CLSC) under the reward-penalty mechanism(RPM), and then respectively develops the centralized and decentralized closed-loop supply chain decision models under penalty mechanism with and without the cost-profit sharing contract. The results show that, with the increase of the reward-penalty intensity, the retail price of product decreases; all the buy-back price, the collection rate and the collector's profit increase, while the manufacturer's profit relates to the target collection rate; with the increase of the cost-sharing ratio and the profit-sharing ratio, the retail price increases, which is always lower than that without the contract, and the collection rate decreases, but is always higher than that without the contract; the buy-back price increases as the cost-sharing ratio increases, while decreases as the profit-sharing ratio increases. The manufacturer can always benefit from the cost-profit sharing contract, but the collector will not accept the contract unless the cost-sharing ratio is mild and the profit-sharing ratio is large. This also indicates that the cost-profit sharing contract takes effect and can coordinate the CLSC in this condition.