We study the symmetry of Cooper pair in a two-dimensional Hubbard model with the Rashbatype spin-orbit interaction as a minimal model of electron gas generated at a heterointerface of SrTiO3/LaAlO3. Solving theÉliashberg equation based on the third-order perturbation theory, we find that the gap function consists of the mixing of the spin-singlet dxy-wave component and the spin-triplet (px ± ipy)-wave one due to the broken inversion symmetry originating from the Rashbatype spin-orbit interaction. The ratio of the d-wave and the p-wave component continuously changes with the carrier concentration. We propose that the pairing symmetry is controlled by tuning the gate voltage.PACS numbers: 74.25.Dw, 74.78.Fk, 71.10.Fd Recent development of technology of epitaxial growth makes it possible to fabricate heterointerface between two different transition-metal oxides. 1,2 The discovery of the generation of two-dimensional electron gas (2DEG) at the n-type heterointerface SrTiO 3 /LaAlO 3 attracts much interest 3 since both SrTiO 3 and LaAlO 3 are band insulators in the bulk material. It is also noted that this 2DEG shows superconductivity with transition temperature T c = 200 mK. 4 This superconductivity differs from the superconductivity of bulk SrTiO 3 with T c = 300 mK in the carrier concentration and the dimensionality of mobile electrons. 5 The discovery of superconductivity is significant since it is promising to control the superconducting states electrically by the applied voltage. Controlling the number of carrier by applied voltage in superconductors is one of the intriguing issues to understand the mechanism of the superconductivity. In cuprates, a superconducting region is located next to an antiferromagnetic phase in an n-T phase diagram. However, in cuprate superconductors, it is not easy to tune the number of carrier by external fields such as the magnetic field or the gate voltage since the number of carrier depends on material compositions. On the other hand, the carrier number of 2DEG at the heterointerface SrTiO 3 /LaAlO 3 can be tuned by the gate voltage since the carrier is generated by the polar and unpolar nature of LaAlO 3 and SrTiO 3 , respectively. 6 Actually, electrostatically tuned superconductor-metal-insulator transition was found to be accessible. 7,8,9 When the electron correlations (Coulomb interaction) are responsible to the superconductivity, the pairing symmetry depends on the number of carrier: The spin-triplet p-wave pairing is favored at low density, 10,11,12,13,14 while on the other hand, the spin-singlet d x 2 −y 2 -wave pairing is favored near half filling. 15,16 Thus, at the heterointerface of oxides with large Coulomb interaction, the phase transition between the spin-singlet and spin-triplet states can be observed by the applied voltage.Another characteristic feature at the heterointerface is lack of the inversion symmetry along the direction perpendicular to the interface (z-axis), which induces the asymmetric spin-orbit interaction called the Rashbatype spin-orbit intera...