This paper presents a functional interval estimation method for continuous-timesystems subject to disturbances and noise. First, a robust functional observer is synthesised to attenuate the effects of uncertainties. Then, based on interval analysis, an interval-based method is proposed to achieve tight functional interval estimation. The proposed method can provide accurate functional interval estimation results for continuous-time systems without using the stringent cooperativity condition and the traditionally required condition on the time derivative of the measurement noise. Simulation results are given to illustrate the effectiveness and superiority of the proposed method.