In this paper, we address the problem of downlink resource allocation and admission control for an Orthogonal Frequency Division Multiple Access (OFDMA)-based Cloud Radio Access Network (C-RAN). Specifically, we formulate the resource allocation and admission control for mobile users in C-RAN as an optimization problem, subject to constraints on mobile users data rate requirements, maximum transmission power and fronthaul links capacity. By dropping the non-linear constraint and reformulating the problem linearly using the framework of the well-known big-M method, we propose a two-stage algorithm that can efficiently solve it. To satisfy the strict timing requirement of wireless communications in such a system, a time constraint was added to our algorithm. Numerical results demonstrate the good performance of our proposal in terms of number of accepted users and total transmission power, when compared with state-of-the-art methods used for the control admission task in C-RAN.