The problem of designing an observer for a linear time-invariant system with delayed measurements of the state is revisited in this paper. The delay is assumed to be time-varying with finite unknown lower and upper bounds. A Gramian-based observer is proposed with a fixed-time convergence rate to a ball. The efficiency of the obtained solution is illustrated by a numerical comparison with linear observers (one of which is tuned under the assumption that a nominal value of delay is available).