  We present in this paper an approach to estimate the initial Lorentz factor
of gamma-ray bursts (GRBs) without referring to the delayed emission of the
early afterglow. Under the assumption that the afterglow of the bursts
concerned occurs well before the prompt emission dies away, the Lorentz factor
measured at the time when the duration of the prompt emission is ended could be
estimated by applying the well-known relations of GRB jets. With the concept of
the efficiency for converting the explosion energy to radiation, this Lorentz
factor can be related to the initial Lorentz factor of the source. The
corresponding rest frame peak energy can accordingly be calculated. Applying
this method, we estimate the initial Lorentz factor of the bulk motion and the
corresponding rest frame spectral peak energy of GRBs for a new sample where
the redshift and the break time in the afterglow are known. Our analysis shows
that, in the circumstances, the initial Lorentz factor of the sample would peak
at 200 and would be distributed mainly within $(100,400)$, and the peak of the
distribution of the corresponding rest frame peak energy would be $0.8keV$ and
its main region would be $(0.3keV,3keV)$.
