This study studies how impulses affect the bounded behaviours of delay system with bounded disturbance. By employing the method of Lyapunov function, several criteria of finite-gain <alternatives>$\mathcal {L_\infty }$<mml:math overflow="scroll"><mml:mrow><mml:msub><mml:mi mathvariant="script">L</mml:mi><mml:mi mathvariant="normal">∞</mml:mi></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href="IET-CTA.2016.1373.IM2.gif" /></alternatives> stability from disturbance to output are established. It is shown that a linear delay differential system can be finite-gain <alternatives>$\mathcal {L_\infty }$<mml:math overflow="scroll"><mml:mrow><mml:msub><mml:mi mathvariant="script">L</mml:mi><mml:mi mathvariant="normal">∞</mml:mi></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href="IET-CTA.2016.1373.IM3.gif" /></alternatives> stabilised from disturbance to output using impulsive feedback control even there is an unstable matrix. Moreover, delay differential equations also maybe finite-gain <alternatives>$\mathcal {L_\infty }$<mml:math overflow="scroll"><mml:mrow><mml:msub><mml:mi mathvariant="script">L</mml:mi><mml:mi mathvariant="normal">∞</mml:mi></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href="IET-CTA.2016.1373.IM4.gif" /></alternatives> stable from disturbance to output under an appropriate sequence of impulses treated as disturbances. Two examples and simulations are also given to illustrate our results.