HyperText Transfer Protocol (HTTP) adaptive streaming (HAS) has undoubtedly become the most cost-effective solution in delivering video contents over the IP networks. While many works have been proposed to improve the performance of HAS, the HAS in the cellular networks is still a challenging problem due to the limited radio resource and the dramatically increasing need for the mobile video service. Specifically, the main problem comes from the incongruous behaviors between rate adaptation and resource allocation. The centralized scheme is a good choice to solve this problem, which determines rate adaptation of all the clients at the base station. However, the existing schemes still have three main weaknesses: 1) poor performance in playout continuity; 2) synchrony in requesting; and 3) low efficiency of radio resource. In this paper, a playout continuity driven framework (PCDF) is proposed to tackle all these drawbacks. First of all, an optimization problem is formulated to optimize the multiclient HAS over long-term evolution network. Then, a PCDF is proposed to solve the problem, which consists of three main features. First, a requesting set is defined to make clients request in a partially synchronous manner, which can not only eliminate the drawback of synchrony but also take advantage of the centralized manner. Second, we propose a two-step resource allocation scheme, of which the two steps work in different temporal scales and cooperate to improve the efficiency of radio resource. Third, with the requesting set and resource allocation, the original optimization problem can be simplified, while it is still NP hard. To solve the problem, we propose a dynamic programming approach, with which the optimal solution can be obtained in polynomial time. Moreover, a greedy algorithm is proposed to decrease the complexity. The experimental results of PCDF demonstrate that the proposed framework can both effectively shorten the playout interruption duration and improve the frame quality in various circumstances.