  We theoretically investigate possible photoinduced topological phase
transitions in the organic salt $\alpha$-(BEDT-TTF)$_2$I$_3$, which possesses a
pair of inclined massless Dirac-cone bands between the conduction and valence
bands under uniaxial pressure. The Floquet analyses of a driven tight-binding
model for this material reveal rich photoinduced variations of band structures,
Chern numbers, and Hall conductivities under irradiation with elliptically
polarized light. The obtained phase diagrams contain a variety of
nonequilibrium steady phases, e.g., the Floquet Chern insulator, Floquet
semimetal, and Floquet normal insulator phases. This work widens a scope of
target materials for research on photoinduced topological phase transitions and
contributes to development of research on the optical manipulations of
electronic states in matters.
