Abstract Recently, the Federal Communications Commission has proposed to create Citizens Broadband Radio Service (CBRS) with the three-tier spectrum sharing system to release more spectrum for the mobile broadband usage in the United States. At the moment, the Wireless Innovation Forum is involved in defining the operational and functional requirements for this framework based on [1], and also in standardizations. Evidently, the successful operation of this system depends on efficient channel allocation algorithms. In this paper, we consider the CBRS with the three-tier spectrum sharing system. A set of CBRS users, i.e., Priority Access License (PAL) and General Authorized Access (GAA) users are located in an area, which is divided into multiple census tracts. The PAL and GAA users request frequency channels from the spectrum access system (SAS). The role of the SAS is to allocate channels to these two types of users while providing interference protection to the incumbent users. For this setup, we consider the problem of channel allocation for PAL and GAA users. The objective is to allocate channels for these two types of users, while considering the channel allocation rules proposed in [1]. For this problem, we propose a channel allocation algorithm to be used by the SAS. The proposed algorithm allocates channels to the CBRS users in two steps: 1) allocate channels to the PAL users and 2) allocate channel to the GAA users. Numerically, we show that the proposed algorithm is able to allocate channels while satisfying the rules proposed in [1]. More importantly, this research provides new insights on investigating channel allocation algorithms in CBRS/SAS.