A general theory of polymer adsorption at a semi-permeable oil-water interface of the biphasic solution is presented. The configurational factor of the solution in the presence of the semi-open boundary at the interface is evaluated by the quasicrystalline lattice model. The present theory gives the feature of the bulk concentration equilibria between oil-water subsystems and the surface excesses of ${Gamma}^{alpha}$ and ${Gamma}^{beta}$ of the polymer segments as a function of the degree of polymerization $gamma$, the Flory-Huggins parameter in $eta$-phase $x_{ ho}^{{eta}_{ ho}}$, the differential adsorption energy parameter in $eta$-phase $x_{sigma}^{{eta}_{ ho}}$, the differential interaction energy parameter ${Delta}x_{ ho}$ and the bulk concentration of the polymer in ${eta}-phase ${varphi}_2^{{eta(*)}_2}$. From our numerical results, the characteristics of ${Gamma}^{alpha}$ are shown to be significantly different from those of ${Gamma}^{eta}$ in the case of high polymers, and this would be the most apparent feature of the adsorption behavior of the polymer at a semi-permeable oil-water interface, which is sensitively dependent on ${Delta}x_{ ho}$ and r.