Abstract This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with multiple packet dropouts. Based on a packet dropout model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are computed recursively in terms of the solution of a Riccati difference equation of dimension equal to the order of the system state plus that of the measurement output. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. Simulation results show the effectiveness of the proposed optimal linear estimators.