The minimax robust Kalman estimation problem is addressed for systems with uncertain noise variance and multistep random measurement delays. A set of Bernoulli distributed random variables with known probability is used to describe the multistep random measurement delays from sensors to estimators. The Hadamard product is used to improve the fictitious noise method, then the original system is converted into one only with uncertain fictitious noise variance. The robust steady-state Kalman predictor, filter and smoother are designed based on the minimax robust estimation principle. The robustness is proved using the Lyapunov equation method, Gerŝgorin circle theorem and matrix elementary transformation. For all admissible uncertainties, the actual estimation error variance is guaranteed to have minimal upper bound. The accuracy relation of conservative and actual estimators is proved. A simulation example of the F-404 aircraft engine system illustrates the effectiveness of the proposed method.