This paper first discusses the H-infinity control problem for a class of general nonlinear Markovian jump systems from the viewpoint of geometric control theory. Following with the updating of the Markovian jump mode, the appropriate diffeomorphism can be adopted to transform the system into special structures, which establishes the basis for the geometric control of nonlinear Markovian jump systems. Through discussing the strongly minimum-phase property or the strongly gamma-dissipativity of the zero-output dynamics, the H-infinity control can be designed directly without solving the traditional coupled Hamilton-Jacobi inequalities. A numerical example is presented to illustrate the effectiveness of our results.