In this study, a new design approach of observers with multiple integrals is presented for descriptor systems, which allows us to decouple or attenuate measurement output disturbances. New design schemes of pure integral observers and proportional integral observers are both investigated, and the measurement noise and the input disturbance are also taken into account simultaneously in this design. In particular, a systematic design procedure of causal or normal multiple-integral observer is addressed, which can be implemented conveniently by Matlab software.The considered disturbance may be unbounded,such that the present design approach is suitable for more general cases. Moreover,the system state, together with the disturbance vector and its finite times derivatives can be estimated simultaneously, the present design then has great potentials in control applications, e.g., diagnosis or observer-based control. The design approaches have nice estimation robustness and can be applied to normal systems directly. Finally, the simulation results show the excellent tracking performance compared to the known results for descriptor systems.