  We have investigated the transition temperature $T_{\rm c}(H)$ of
superconductiv ity in quasi-two-dimensional (Q2D) tight-binding electrons in a
strong magnetic field. When the magnetic field is parallel to 2D conducting
plane, $T_{\rm c}(H) $ of the Q2D superconductor is shown to increase in an
oscillatory manner as the magnetic field becomes large and to reach $T_{\rm
c}(0)$ in a strong magnetic f ield limit for the spin-triplet superconductor.
We consider the cases of on-site and nearest sites attractive interaction, and
calculate the magnetic field depe ndences of the transition temperature for
various 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 is
parallel to the $y$ direction, which will be observed in a triplet
superconductor, Sr$_2$RuO$_4$.
