  The difference of the moment of inertia of the neutron star PSR J0348 + 0432
and that of its proto neutron star is studied in the framework of the
relativistic mean field theory considering baryon octet. The temperature of the
proto neutron star PSR J0348+0432 is chosen as T=5 MeV. The calculations show
that the central baryon number density of the proto neutron star PSR J0348+0432
is in the range 0.623$\sim$0.813 fm$^{-3}$, decreased by 2$\sim$7\% compared to
that of the neutron star PSR J0348+0432. The radius of the proto neutron star
PSR J0348+0432 is in the range 13.101$\sim$12.419 km, increased by 1$\sim$2\%
compared to that of the neutron star PSR J0348+0432. The moment of inertia of
the proto neutron star PSR J0348+0432 is in the range
1.939$\times$10$^{45}$$\sim$1.638$\times$10$^{45}$ g.cm$^{2}$, increased by
about 2$\sim$7\% compared to that of the neutron star PSR J0348+0432.
