In this letter, an integrated sensing and communication (ISAC) system is considered, with a dual function base station designated to serve communication users while sensing interested targets. To enhance throughput and spectrum efficiency, the sum weighted bit rate is maximized to guarantee the effective sensing power through beamforming design. To tackle the non-convexity of the original optimization problem, an alternating optimization algorithm which efficiently combines fractional programming (FP) with successive convex approximation (SCA) is proposed. Specifically, when the non-convex constraint is approximated by SCA as the difference between an affine function and a constant, the remaining non-convex beamforming design problem is equivalently transformed and can be solved by FP. Simulations results validate the superiority of the proposed algorithm in improving the communication performance while ensuring sensing performance.