The future sixth generation (6G) wireless communications look forward to constructing a ubiquitous intelligent information network with high data rates. To fulfill such challenging visions, the reconfigurable holographic surface (RHS) is developed as a promising solution due to its capability of accurate multi-beam steering with low power consumption and hardware cost. Different from the conventional phase-controlled antennas, the RHS can control the radiation amplitude of the reference wave propagating on the metasurface by leveraging the holographic technique. The desired object waves can then be generated without complex phase-shifting circuits, enabling the convenient implementation of the transceiver. Such amplitude-controlled holographic beamforming triggers new challenges since a new beamforming scheme needs to be developed to handle the complex-domain optimization problem subject to the unconventional real-domain amplitude constraints, which makes the superposition of the radiation waves from different antenna elements difficult to tackle. In this letter, we consider an RHS-aided multi-user communication system with a base station equipped with an RHS. We formulate a sum rate maximization problem and design a novel amplitude-controlled algorithm to solve the problem. Simulation results verify the effectiveness of the proposed scheme.