A dispersion relation is derived for the collective oscillation mode in a strongly correlated electron system, described by a single-band lattice Hubbard model. On the basis of the equations of motion for a pair of propagators (oneand two-electron causal temperature Green functions), a self-oscillatory condition is formulated and obtained by the same technique as the superconductor susceptibility to a variable external field. The equations of motion are subdivided into a stationary part and an oscillatory part. The stationary part establishes a self-consistent relation between the chemical potential and the occupancy numbers of the thermodynamic equilibrium state, and it can be applied to any variously ordered a priori ground state. The oscillatory part yields a dispersion relation for the collective oscillation mode, and it is considered for a system with translationally invariant ground state.