Effect of the interaction between hyperons on the moment of inertia of proto neutron stars (PNSs) PSR J0740+6620, PSR J0348+0432, PSR J1614-2230 and PSR J0737-3039A is examined by means of relativistic mean field theory. Taking into account the interaction between hyperons, the mass M of the PNS decreases with respect to the same radius R, the energy density ε increases with respect to the same pressure p, and the moment of inertia I of the PNS decreases with respect to the same central energy density ε c . Under the constraint of the mass of the PNS, considering the interaction between hyperons, the larger the mass of the PNS, the more the radius and moment of inertia of the PNS decrease, while the more energy density and pressure increase. For smaller PNSs, the effect can be negligible.