In this paper, we propose a null-space compensation control for linear first-order systems with redundant two input channels. In the input redundant systems, control input vector generally has null-space component of the plant parameter vector. The null-space component does not contribute to the generation of the control force which drives the plant state. If a control input that does not include the null-space component can be generated, efficient control is achieved from the viewpoint of minimizing the norm of the control input. In the proposed method, an adaptive control method is used to design a control system that compensates for the null-space component, even if the plant parameter vector is unknown. The effectiveness is shown by numerical examples.