  We consider the Standard Model with a new scalar field $X$ which is a
$n_X^{}$ representation of the $SU(2)_L$ with a hypercharge $Y_X$. The
renormalization group running effects on the new scalar quartic coupling
constants are evaluated. Even if we set the scalar quartic coupling constants
to be zero at the scale of the new scalar field, the coupling constants are
induced by the one-loop effect of the weak gauge bosons. Once non-vanishing
couplings are generated, the couplings rapidly increase by renormalization
group effect of the quartic coupling constant itself. As a result, the Landau
pole appears below Planck scale if $n_X^{}\geq 4$. We find that the scale of
the obtained Landau pole is much lower than that evaluated by solving the
one-loop beta function of the gauge coupling constants.
