This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible the largest delay is bounded. Based on this new model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. The steady-state estimators are also investigated.A sufficient condition for the convergence of the optimal linear estimators is given. A simulation example shows the effectiveness of the proposed algorithms.