In this study, the problem of sequential fusion <alternatives>$\mathcal {H}_\infty $<mml:math overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:msub></mml:math><inline-graphic xlink:href="IET-CTA.2016.1014.IM2.gif" /></alternatives> filtering is investigated for multi-rate multi-sensor time-varying systems based on a Krein-space approach. The considered system is with different evolving rate of the state and the estimation as well as measurement sampling rates. A novel performance index is proposed to sequentially characterise the effect of system noise on the fusion estimate errors. Based on the augmented measurement including all received measurements, a sequential fusion <alternatives>$\mathcal {H}_\infty $<mml:math overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:msub></mml:math><inline-graphic xlink:href="IET-CTA.2016.1014.IM3.gif" /></alternatives> filter is derived by solving a positive minimisation problem of an indefinite quadratic form, such that the new performance index is ensured. Furthermore, a recursive projection method is proposed in the Krein space to reduce the computation burden. Then, a recursive sequential fusion filter is given to ensure that the minimum value is positive. Finally, two simulation examples are given to illustrate the advantages of the proposed methods.