A new deadbeat control scheme for linear systems with input constraints is presented. Input constraints exist in most control systems, but in conventional dead-beat control, logical strategy to handle it has not been studied enough. The proposed controller in this paper adjusts the number of steps for dead-beat tracking on-line, in order to achieve delayed deadbeat-tracking performance and satisfy any admissible input constraint. Increasing the number of steps for dead-beat tracking and formulating the corresponding degree of freedom into null-space vectors make it possible to obtain delayed dead-beat tracking, and minimize the inevitable delay, respectively. LMI feasibility problems are solved to numerically obtain the solution and minimize the unavoidable step-delay. As a result, calculation effort is reduced compared to LMI-optimization problem. The proposed schemes can be readily numerically implemented. Its practical usefulness is validated by simulation for 6-axis robot model and experimental results for DC-motor servoing.