The effect of interaction between hyperons on the moment of inertia of proto neutron star (PNS) PSR J0740+6620 is examined with relativistic mean field theory considering the octet of baryons. The nucleon coupling constant GM1 is used and the temperature of the PNS is chosen as T = 20 MeV. Under the constraint of the mass M = 2.08 M ⊙ , considering the interaction between hyperons, the radius of the PNS PSR J0740+6620 is reduced by 0.08% from R = 14.518 km to R = 14.507 km and the moment of inertia of the PNS PSR J0740+6620 is reduced by about 0.49% from I = 2.460 × 10 45 g  cm 2 to I = 2.448 × 10 45 g cm 2 , respectively. The moment of inertia of the PNS has a peak with the change of central energy density ε c , mass M or radius R . Considering the interaction between hyperons, the value of the moment of inertia I of the PNS corresponding to this peak will decrease.