We study the dynamical energy equipartition properties in the integrable Toda model with additional uniform or disordered on-site energies by extensive numerical simulations.The total energy is initially equidistributed among some of the lowest frequency linear modes.For the Toda model with uniform on-site potentials,the energy spectrum keeps its profile nearly unchanged in a relatively short time scale.On a much longer time scale,the energies of tail modes increase slowly with time.Energy equipartition is far away from being attached in our studied time scale.For the Toda model with disordered on-site potentials,the energy transfers continuously to the high frequency modes and eventually towards energy equipartition.We further perform a systematic study of the equipartition time teq depending on the energy density ε and the nonlinear parameter α in the thermodynamic limit for the Toda model with disordered on-site potentials,We find teq∝ (1/ε)a(1/α)b,where b ≈ 2a.The values of a and b are increased when increasing the strengths of disordered on-site potentials or decreasing the number of initially excited modes.