In this technical note, the H-infinity control problem for a class of discrete-timeMarkov jump systems (MJSs) with uncertain transition probabilities (TPs) is investigated. The uncertain information of transition probabilities is quantized by Gaussian transition probability density function (pdf). In light of the proposed descriptions, the MJSs with Gaussian PDF of TPs cover the systems with precisely known and partially known TPs as two special cases. Sufficient conditions for the existence of H-infinity controller of the underlying systems are derived in term of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.