The stability of the linear chain structure of three α clusters for 12 C against the bending and fission is investigated in the cranking covariant density functional theory, in which the equation of motion is solved on a 3D lattice with the inverse Hamiltonian and the Fourier spectral methods.Starting from a twisted three α initial configuration, it is found that the linear chain structure is stable when the rotational frequency is within the range of ∼2.0 MeV to ∼2.5 MeV. Beyond this range, the final states are not stable against fission. By examining the density distributions and the occupation of single-particle levels, however, these fissions are found to arise from the occupation of unphysical continuum with large angular momenta. To properly remove these unphysical continuum, a damping function for the cranking term is introduced. Eventually, the stable linear chain structure could survive up to the rotational frequency ∼3.5 MeV, but the fission still occurs when the rotational frequency approaches to ∼4.0 MeV.