The properties of proto neutron star (PNS) PSR J0737-3039A is studied by using relativistic mean field theory. Five sets of nucleon coupling constants (DD-MEI, GL85, GL97, GM1 and NL2) are used. Using these five sets of nucleon coupling constants, the radius of the PNS PSR J0737-3039A is $R$=15.693-18.846 km, the central baryon density is $\rho_{c}$=0.247-0.359 fm$^{-3}$, the central energy density is $\varepsilon_{c}$=4.30$\times$10$^{14}$-6.49$\times$10$^{14}$ g.cm$^{-3}$, and the central pressure is $p_{c}$=3.79$\times$10$^{34}$-5.85$\times$10$^{34}$ dyne.cm$^{-2}$. For DD-MEI, GL85, GL97 and GM1, baryons octet all appear in the PNS PSR J0737-3039A. By NL2, only baryons n, p, $\Lambda$, $\Sigma^{0}$, $\Sigma^{-}$, $\Xi^{0}$ and $\Xi^{-}$ are present. Corresponding to the same baryon density, the relative densities of the same baryon in the PNS PSR J0737-3039A calculated from different nucleon coupling constants differ greatly. The central relative baryon densities of the PNS PSR J0737-3039A calculated by different nucleon coupling constants also differ greatly.