The design of a multi-constrained full-order fault estimation observer (FFEO) with finite frequency specifications is studied for continuous-time systems. By constructing an augmented system, a multi-constrained FFEO in finite frequency domain is proposed to achieve fault estimation. Meanwhile, the presented FFEO can avoid the overdesign problem generated by the entire frequency domain by the generalised Kalman-Yakubovich-Popov lemma. Furthermore, by introducing slack variables, improved results on FFEO design in different frequency domains are obtained such that different Lyapunov matrices can be separately designed for each constraint. Simulation results are presented to demonstrate the effectiveness and potentials of the proposed techniques.