  The Vela pulsar represents a distinct group of {\gamma}-ray pulsars. Fermi
{\gamma}-ray observations reveal that it has two sharp peaks (P1 and P2) in the
light curve with a phase separation of 0.42 and a third peak (P3) in the
bridge. The location and intensity of P3 are energy-dependent. We use the 3D
magnetospheric model for the annular gap and core gap to simulate the
{\gamma}-ray light curves, phase-averaged and phase-resolved spectra. We found
that the acceleration electric field along a field line in the annular gap
region decreases with heights. The emission at high energy GeV band is
originated from the curvature radiation of accelerated primary particles, while
the synchrotron radiation from secondary particles have some contributions to
low energy {\gamma}-ray band (0.1 - 0.3 GeV). The {\gamma}-ray light curve
peaks P1 and P2 are generated in the annular gap region near the altitude of
null charge surface, whereas P3 and the bridge emission is generated in the
core gap region. The intensity and location of P3 at different energy bands
depend on the emission altitudes. The radio emission from the Vela pulsar
should be generated in a high-altitude narrow regions of the annular gap, which
leads to a radio phase lag of ~ 0.13 prior to the first {\gamma}-ray peak.
