  It has been thought that narrow-line Seyfert 1 galaxies are likely to be in
the early stages of the evolution of active galaxies. To test this suggestion,
the ratios of the central massive black hole (MBH) mass to the bulge mass
($M_{\rm bh}/M_{\rm bulge}$) were estimated for 22 Narrow Line AGNs (NL AGNs).
It is found that NL AGNs appear to have genuinely lower MBH/Bulge mass ratio
($M_{\rm bh}/M_{\rm bulge}$). The mean $ log(M_{\rm bh}/M_{\rm bulge})$ for 22
NL AGNs is $-3.9\pm 0.07$, which is an order of magnitude lower than that for
Broad Line AGNs and quiescent galaxies. We suggest a nonlinear MBH/Bulge
relation and find there exists a relation between the $M_{\rm bh}/M_{\rm
bulge}$ and the velocity dispersion, $\sigma$, derived from the [O ${\rm \small
III}$] width. A scenario of MBH growth for NL AGNs is one of our
interpretations of the nonlinear MBH/Bulge relation. The MBH growth timescales
for 22 NL AGNs were calculated, with a mean value $(1.29\pm0.24)\times 10^{8}$
yr. Another plausible interpretation is also possible: that NL AGNs occur in
low-$M_{\rm bulge}$ galaxies and that in such galaxies $M_{\rm bh}/M_{\rm
bulge}$ is lower than that in galaxies with a higher $M_{\rm bulge}$, if we
consider that NL AGNs already have their ``final'' $M_{\rm bh}/M_{\rm bulge}$.
More information of the bulge in NL AGNs is needed to clarify the black hole --
bulge relation.

Astrophysics