© 2020 John Wiley & Sons Ltd This study, under zero initial condition, aims to characterize the reachable set bound for a class of neutral Markovian jump systems (NMJSs) with interval time-varying delays and bounded disturbances. To begin with, the time-delays are considered to be mode-dependent while delay mode and system mode are different. By utilizing free-weighting matrix method and reciprocally convex combination technique, an ellipsoid-like bound is characterized for the concerned NMJS with completely known transition probabilities. Based on the provided analytical framework, the case of same delay mode and system mode is also handled. Then, benefitting from a group of free-connection weighting matrices, the reachable set estimation issue is tackled for the NMJS involving mode-independent time-varying delays and partially known transition probabilities. The theoretical analysis is confirmed by numerical simulations.