  To explain the matter-antimatter asymmetry in the Zee-Babu (ZB) model, the
sphaleron process in the baryogenesis scenario is calculated. It always
satisfies the de-coupling condition and the strength of phase transition ($S$)
is always greater than $1$ in the presence of triggers other than that in the
Standard Model, which are singly ($h^{\pm}$) and doubly ($k^{\pm\pm}$) charged
scalar bosons. Sphaleron energies are in the range of 5-10 TeV, in calculation
with bubble profiles containing free parameters and assuming nuclear bubbles of
$h^{\pm}$ and $k^{\pm\pm}$ are very small. We tested the scaling law of
sphaleron again with an average error of $10\%$. When the temperature is close
to the critical one ($T_c$), the density of nuclear bubble is produced very
large and decreases as the temperature decreases. The key parameter is $\alpha$
which results in the gravitational wave density parameter ($\Omega h^2$) in the
range of $10^{-14}$ to $10^{-12}$ when $\beta/H^*=22.5$, this is not enough to
detect gravitational waves from electroweak phase transition (EWPT) according
to the present LISA data but may be detected in the future. As the larger
strength of phase transition is, the more $\alpha$ increases (this increase is
almost linear with $S$), the larger the gravitational wave density parameter
is. Also in the context of considering the generation of gravitational waves,
in the ZB model we calculated $\alpha \sim \text{a few} \times 10^{-2}\ll 1$,
so rigorously conclude that the EWPT is not strong even though $S>1$. We also
suggest that, for a model with a lot of extra scalar particles and particles
which play a role in mass generation, the stronger the EWPT process and the
larger $\Omega h^2$ can be.
