Constant frequency average current mode (ACM) control is a widely used control scheme for converters requiring precise current control. However, its transient response is relatively slow, while the switching loss and driving loss significantly diminish the light load efficiency. To solve these issues, the I2 control ACM is proposed. By combining the fast direct current feedback and integral feedback, the I2 control achieves both wide bandwidth and accurate current control. As a particular embodiment of this concept, by adopting constant on-time modulation, constant on-time I2 control needs no artificial ramp, and has a fast dynamic response. Moreover, due to the decrease of the switching frequency, constant on-time I2 control improves the efficiency in discontinuous conduction mode. The concept of I2 control can be extended to other modulations. A small-signal model using the describing-function-based equivalent circuit model is proposed. The model is accurate up to 1/2 switching frequency. Based on the model, the design guidelines are discussed. The proposed control is verified with simulation and hardware measurement results.