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We have investigated the transition temperature $T_{\rm c}(H)$ ofsuperconductiv ity in quasi-two-dimensional (Q2D) tight-binding electrons in astrong magnetic field. When the magnetic field is parallel to 2D conductingplane, $T_{\rm c}(H) $ of the Q2D superconductor is shown to increase in anoscillatory manner as the magnetic field becomes large and to reach $T_{\rmc}(0)$ in a strong magnetic f ield limit for the spin-triplet superconductor.We consider the cases of on-site and nearest sites attractive interaction, andcalculate the magnetic field depe ndences of the transition temperature forvarious types of symmetry. The first o rder transition from $p_y$-wave to$p_x$-wave is shown to occur at $H\sim 35$T w hen the magnetic field isparallel to the $y$ direction, which will be observed in a tripletsuperconductor, Sr$_2$RuO$_4$.Comment: 13pages,6figure

Superconductivity of Quasi-Two-Dimensional Tight-Binding Electrons in a Strong Magnetic Field