In this note, a modified-likelihood Bayesian filter is proposed for a class of discrete-time nonlinear dynamical systems whose outputs are transmitted to the estimator with random delay and dropout. The likelihood function of the filter is computed by marginalizing out the delay variable to extract accurate information from the delayed measurements. Moreover, the measurement update stage of the filtering algorithm is omitted when no new measurement is received. Simulation results are presented to verify the superior performance of the introduced filter compared to some existing ones in the literature. (C) 2019 Elsevier Ltd. All rights reserved.