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General high-order rogue waves of the NLS-Boussinesq equation are obtained bythe KP-hierarchy reduction theory. These rogue waves are expressed with thedeterminants, whose entries are all algebraic forms. It is found that thefundamental rogue waves can be classified three patterns: four-petals state,dark state, bright state by choosing different parameter $\alpha$ values. Asthe evolution of the parameter $\alpha$. An interesting phenomena isdiscovered: the rogue wave changes from four-petals state to dark state,whereafter to the bright state, which are consistent with the change of thecorresponding critical points to the function of two variables. Furthermore,the dynamics of second-order and third-order rogue waves are presented indetail, which can be regarded as the nonlinear superposition of the fundamentalrogue waves.

General high-order rogue wave to NLS-Boussinesq equation with the dynamical analysis