It is crucial to estimate the location of primary users (PUs) for the development of cognitive radio networks (CRNs). Great efforts have been made in the past to develop localization algorithms with better accuracy but low computation. In CRNs, PUs do not cooperate with secondary users (SUs), which makes the localization task challenging. Due to this feature, received signal strength (RSS)-based PU localization techniques, such as centroid localization (CL) and multidimensional scaling (MDS), are the best candidates. However, most of the CL- and MDS-based PU localization methods consider omnidirectional wireless communication. Therefore, in this paper we propose a PU localization method which uses the RSS values at different sectors of the SU antenna, where a scoring strategy is applied to all the sectors to estimate the PU location. Two different scoring functions are proposed. Numerical results show that the proposed localization method is robust to PU locations and channel conditions. The proposed method is validated in terms of various network parameters, such as the number of SUs, beamwidth of the SU sectors, size of the grid, and placement of the PUs. Results show that increasing the number of SUs improve the localization accuracy due to an increased number of measurements. However, the localization accuracy degrades with an increase in the beamwidth of the SU sector because the faraway grid points also participate in the localization. The results are also compared with the conventional CL for PU localization. Compared with conventional CL, it offers a significant improvement in the performance.