  We report an investigation of the structure of $^{12}$C nucleus employing a
newly developed configuration-mixing method. In the three-dimensional
coordinate-space representation, we generate a number of Slater determinants
with various correlated structures using the imaginary-time algorithm. We then
diagonalize a many-body Hamiltonian with the Skyrme interaction in the space
spanned by the Slater determinants with parity and angular momentum
projections. Our calculation reasonably describes the ground and excited states
of $^{12}$C nucleus, both for shell-model-like and cluster-like states. The
excitation energies and transition strengths of the ground-state rotational
band are well reproduced. Negative parity excited states, $1_1^-$, $2_1^-$, and
$3_1^-$, are also reasonably described. The second and third $0^+$ states,
$0_2^+$ and $0_3^+$, appear at around 8.8 MeV and 15 MeV, respectively. The
$0_2^+$ state shows a structure consistent with former results of the
\alpha-cluster models, however, the calculated radius of the $0_2^+$ state is
smaller than those calculations. The three-{\alpha} linear-chain configuration
dominates in the $0_3^+$ state.
