  We investigate the GRB formation rate based on the relation between the
spectral peak energy ($E_{p}$) and the isotropic luminosity. The
$E_{p}$--luminosity relation covers the energy range of 50 -- 2000 keV and the
luminosity range of $10^{50}$--$10^{54} erg/s, respectively. We find that the
relation is considerably tighter than similar relations suggested previously.
Using $E_{p}$--luminosity relation, we estimate the luminosity and the redshift
of 684 GRBs with the unknown distances and derive the GRB formation rate as a
function of the redshift. For $0 \le z \le 2$, the GRB formation rate is well
correlated with the star formation rate while it increases monotonously from
$z\sim 2$ out to $z \sim 12$. This behavior is consistent with the results of
previous works using the lag--luminosity relation or the
variability--luminosity relation.
