The possibility of laser cooling the 24Mg35Cl molecule is investigated using the electronic, rovibrational, and hyperfine structure. Twelve low-lying Λ-S electronic states of the 24Mg35Cl 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 A2Π → X2Σ+ transition and short radiative lifetime of the A2Π state are determined. Then, employing a quantum effective Hamiltonian approach, we investigate the hyperfine manifolds of the X2Σ+ 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 24Mg35Cl molecule. Moreover, it is important to note that the dissociation energy (2.2593 eV) of the B2Σ+ 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.