  A new theoretical method is proposed to describe the ground and excited
cluster states of atomic nuclei. The method utilizes the equation-of-motion of
the Gaussian wave packets to generate the basis wave functions having various
cluster configurations. The generated basis wave functions are superposed to
diagonalize the Hamiltonian. In other words, this method uses the real time as
the generator coordinate. The application to the $3\alpha$ system as a
benchmark shows that the new method works efficiently and yields the result
consistent with or better than the other cluster models. Brief discussion on
the structure of the excited $0^+$ and $1^-$ states is also made.
