A grey stochastic multiple criteria decision-making method based on the kernel and degree of greyness of grey heterogeneous data is proposed for the stochastic multiple criteria decision problem with criterion value as grey heterogeneous data. The definitions of greyness of the extended grey number and grey heterogeneous data sets are given. Then, the kernel vector and greyness vector of grey heterogeneous data are defined according to the principle of information utilization and combining with the common characteristics of grey heterogeneous data. Furthermore, the consistency coefficient geometric plane die length sorting method and the relative compromise distance sorting method are constructed. An illustrative example illustrates the effectiveness and rationality of the proposed approach.