The electrons confined at the interfacial quantum well of a LaAlO3/SrTiO3 display various exotic condensed matter phases and rich spin-orbitronic functionalities associated with broken inversion symmetry. This 2D polar conductor may exhibit directional propagation of itinerant electrons, i.e. the rightward and leftward currents differ from each other, when the time-reversal symmetry is further broken by applying a magnetic field. This potential rectification effect in general was shown to be very weak due to the fact that kinetic energy is much higher than energies associated with symmetry breakings producing weak perturbation. Here, we present large gate-tunable nonreciprocal magnetoresistance in LaAlO3/SrTiO3 conductive interface, where the electrons are confined at two-dimension with low Fermi energy. The coefficient γ representing the strength of magnetochiral anisotropy, was measured to be as high as ~ 56 T-1A-1, which is about 2 order of magnitude higher than those estimated for typical noncentrosymmetric conductors. The observed directional charge transport shows linear dependence on the applied current, while it exhibits higher order dependence on the applied magnetic field. The behavior of directional response in LaAlO3/SrTiO3 is associated with comparable energy scales among kinetic energy, spin-orbit interaction, and magnetic field, which opens a new route to enhance nonreciprocal response and its functionalities in the emerging spin-orbitronics.