The possibility degree and distance of extended grey numbers are defined. For multi-criteria decision-making problems, where the probabilities are uncertain and the criteria values of alternatives can be extended grey numbers, a grey stochastic multi-criteria decision-making approach based on Hurwicz with uncertain probability is proposed. By using the possibility degree of extended grey number and Hurwicz criteria, the evaluation values of each alternative for each criterion are calculated, and the standard utility value decision matrix can be obtained after normalization. The decision-maker’s perceived value of the gain or loss of every alternative is calculated according to the distance of extended grey number and basic idea of the TODIM method. Then all alternatives are ranked according to the comprehensively perceived values. Finally, an illustrative example shows the feasibility and effectiveness of the proposed approach.