Excited states in the neutron-rich nucleus 12Be were experimentally investigated via α-inelastic scattering. The excited states in the 12Be nucleus were populated by a 12Be(α, α′) reaction at 60 A MeV in the inverse kinematics, and identified by measuring a 6He+6He breakup channel in coincidence. The differential cross section and the angular correlations between the decay particles were obtained for each excitation energy from 10 MeV to 20 MeV, reconstructed by the measured momentum vectors of the two 6He's. A multipole decomposition analysis based on the distorted-wave Born approximation was applied for the angular distribution of the inelastic scattering together with the angular correlation between the decay particles with respect to the directions of the incident beam and to the momentum transfer simultaneously. From the decomposed excitation energy spectra for L=0, 2, and 4, new excited states with Jπ=0+ and Jπ=2+ were identified, which were candidates of the band-head of a largely deformed rotational band. According to their similar energy spacings in J=0 and J=2 energy spectra, these excited states were possibly forming rotational bands with almost same large moments of inertia. The structures of the observed states are discussed with predictions of theoretical models.