The experimental realization of a Kitaev model on the honeycomb lattice has been a major topic in a condensed matter physics, because the model uniquely provides exactly solvable quantum spin liquid ground states with the Majorana fermions. The newly discovered alpha-RuCl3 forming a perfect honeycomb lattice with Ising-like spin interactions has strong indications that it lies in proximate to a Kitaev spin liquid phase. Although the material exhibits antiferromagnetic ordering below 6.5 K, the Kitaev physics in the ordered ground state is still dominantly working, providing remarkable evidences for the Majorana fermion excitations. We propose inelastic neutron scattering on the alpha-RuCl3 single crystal to study the critical behavior of Majorana fermions where it is coupled to local order parameter given by non-Kitaev Hamiltonians, exploring to quantum critical region.