A receding horizon Kalman finite-impulse response (FIR) filter is suggested for continuous-time systems, combining the Kalman filter with the receding horizon strategy. In the suggested filter, the horizon initial state is assumed to be unknown. It can always be obtained irrespective of unknown information on the horizon initial state, The filter may be the first stochastic FIR form for continuous-time systems that may have many good inherent properties. The suggested filter can be represented in an iterative form and also in a standard FIR form. The suggested filter turns out to be a remarkable deadbeat observer. The validity of the suggested filter is illustrated by numerical examples.