This letter proposes robust finite impulse response (FIR) filters for linear continuous-time statespace models with bounded uncertainties. A set of all reachable current states under bounded uncertainties is determined from inputs and outputs on a recent finite time interval. If some condition is met, this set is shown to be represented in an ellipsoidal form. The derivation procedure is much simplified by utilizing the result on the optimal tracking control with an indefinite cost function. In order to minimize the maximum estimation error due to uncertainties, the center of the reachable ellipsoidal set is chosen as an estimated state. It is shown through simulation that the proposed robust FIR filter achieves a more robust performance than existing robust infinite impulse response (IIR) filters.