The H static output feedback control of continuous Markov jump systems with incomplete transition probabilities is investigated in this paper. Employing the property of continuous transition probabilities and a matrix transformation technique, relaxed sufficient conditions for the existence of a solution to the H static output feedback control problem are established in terms of linear matrix inequalities. In addition, the obtained results are extended to Markov jump nonlinear systems. Numerical examples are provided to demonstrate the effectiveness of the derived results.