For linear system with time-domain constraints including control input constraints, state constraints or their mixed constraints, an H∞ control scheme via Linear Matrix Inequalities (LMI) optimization was proposed in this paper. First, by assumption of initial states and the energy of external disturbance, a fixed ellipsoid containing all perturbed feasible trajectories was confirmed. Then, sufficient conditions of the closed-loop system satisfying time-domain constraints with the controller gain varying during a certain scope were derived and converted to LMI, and the derivation process was given in detail. Finally, the non-fragile H∞ controller design with time-domain constraints was led to solving an optimization problem with LMI constraints. Simulation results for application in the disturbance reject problem of mass-spring-damper system were discussed. The simulation application results show that the designed controller can improve the robustness of the closed-cloop system with controller gain variations while the time-domain constraints are respected.