This study addresses the estimation problem for discrete-time measurement-delay systems with multiplicative noise and Markov jump. First, the state equation is converted into two equations according to the geometric arguments and flexible transformations. Then, based on the reorganised innovation approach, the finite-horizon linear minimum mean-square-error estimator is derived in terms of two Riccati difference equations and two Lyapunov difference equations. Finally, under the assumptions of mean square stability of the system and ergodicity of the associated Markov chain, a sufficient condition for the existence of the infinite-horizon estimator is presented. We provide a numerical example to manifest the efficiency of the proposed approach.