  We propose new version of massive $F(R)$ gravity which is natural
generalization of convenient massive ghost-free gravity. Its Hamiltonian
formulation in scalar-tensor frame is developed. We show that such $F(R)$
theory is ghost-free. The cosmological evolution of such theory is
investigated. Despite the strong Bianchi identity constraint the possibility of
cosmic acceleration (especially, in the presence of cold dark matter) is
established. Ghost-free massive $F(R,T)$ gravity is also proposed.
