The possibility of laser cooling the (MgCl)-Mg-24-Cl-35 molecule is investigated using the electronic, rovibrational, and hyperfine structure. Twelve low-lying Lambda-S electronic states of the (MgCl)-Mg-24-Cl-35 molecule have been calculated at the multireference configuration interaction level of theory. The spin-orbit coupling effects are taken into account in the electronic structure calculations. Spectroscopic constants agree well with previously obtained theoretical and experimental values. On the basis of the potential energy curves and transition dipole moments, the highly diagonally distributed Franck-Condon factors for the A(2)Pi -> X-2 Sigma(+) transition and short radiative lifetime of the A(2)Pi state are determined. Then, employing a quantum effective Hamiltonian approach, we investigate the hyperfine manifolds of the X-2 Sigma(+) state and obtain the zero-field hyperfine spectrum with the errors relative to the experimental data not exceeding 8-20 kHz. Finally, we design a laser cooling scheme with one cooling main laser beam and two repumping laser beams with modulated sidebands, which is sufficient for the implementation of efficient laser slowing and cooling of the (MgCl)-Mg-24-Cl-35 molecule. Moreover, it is important to note that the dissociation energy (2.2593 eV) of the B-2 Sigma(+) state is obtained for the first time at the multireference configuration interaction level. We hope that this can provide a helpful reference for experimental observation.