  The 6.7 GHz methanol maser emission, a tracer of forming massive stars,
sometimes shows enigmatic periodic flux variations over several 10-100 days. In
this Letter, we propose that this periodic variations could be explained by the
pulsation of massive protostars growing under rapid mass accretion with rates
of Mdot > 10^-3 Msun/yr. Our stellar evolution calculations predict that the
massive protostars have very large radius exceeding 100 Rsun at maximum, and we
here study the pulsational stability of such the bloated protostars by way of
the linear stability analysis. We show that the protostar becomes pulsationally
unstable with various periods of several 10-100 days, depending on different
accretion rates. With the fact that the stellar luminosity when the star is
pulsationally unstable also depends on the accretion rate, we derive the
period-luminosity relation log (L/Lsun) = 4.62 + 0.98log(P/100 day), which is
testable with future observations. Our models further show that the radius and
mass of the pulsating massive protostar should also depend on the period. It
would be possible to infer such protostellar properties and the accretion rate
with the observed period. Measuring the maser periods enables a direct
diagnosis of the structure of accreting massive protostars, which are deeply
embedded in dense gas and inaccessible with other observations.
