A control system for a construction machine includes a design surface acquisition unit configured to acquire a design surface that indicates a target shape of a construction target, a target value generation unit configured to generate a target value of an amount of control of working equipment, a prediction unit configured to calculate a predicted value of the amount of control of the working equipment based on the target value and a prediction model for the working equipment, and calculate an amount of drive to control the working equipment based on the predicted value and the design surface, and a command unit configured to output a control command for control of the working equipment based on the amount of drive.