For desirable quality of service, content providers aim at covering content requests by large network caches. Content caching has been considered as a fundamental module in network architecture. There exist few studies on the optimization of content caching. Most existing works focus on the design of content measurement, and the cached content is replaced by a new one based on the given metric. Therefore, the performance for service provision with multiple levels is decreased. This paper investigates the problem of finding optimal timer for each content. According to the given timer, the caching policies determine whether to cache a content and which existing content should be replaced, when a content miss occurs. Aiming to maximize the aggregate utility with capacity constraint, this problem is formalized as an integer optimization problem. A linear programming based approximation algorithm is proposed, and the approximation ratio is proved. Furthermore, the problem of content caching with relaxed constraints is given. A Lagrange multiplier based approximation algorithm with polynomial time complexity is proposed. Experimental results show that the proposed algorithms have better performance.