The H-infinity smoothing problem for continuous systems is treated in a state space representation by means of variational calculus techniques. The smoothing problem is introduced in an H. criterion by means of an artificial discontinuity that splits the problem in term of H-infinity forward and H-infinity backward filtering problems. Hence, the smoother design is realized in three steps. First, a forward filter is developed. Secondly, a backward filter is developed taking into account the backward Markovian model. The third step consists of combining the two previous steps in order to compute the H-infinity smoothed estimate. An example shows the efficiency of this proposed smoother.