The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems (MJSs) with parameters uncertainties and multiple time-delays are considered. The delays are respectively considered as constant and time varying, and the uncertain parameters are assumed to be norm bounded. By means of Takagi-Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By selecting the appropriate Lyapunov-Krasovskii functions, the sufficient condition is given such that the uncertain fuzzy neutral MJSs are stochastically stability for all admissible uncertainties and satisfies the given H∞ control index. The stability and H∞ control criteria are formulated in the form of linear matrix inequalities, which can be easily checked in practice. Practical examples illustrate the effectiveness of the developed techniques.