The Vela pulsar represents a distinct group of Delta *g-ray pulsars. Fermi Delta *g-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 three-dimensional magnetospheric model for the annular and core gaps to simulate the Delta *g-ray light curves and the phase-averaged and phase-resolved spectra. We found that the acceleration electric field along a field line in the annular gap region decreases with height. Emission at the high-energy GeV band originates from the synchro-curvature radiation (mainly curvature radiation) of accelerated primary particles, while the synchrotron radiation from secondary particles contributes somewhat to the low-energy Delta *g-ray band (0.1-0.3 GeV). The Delta *g-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 are 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 region of the annular gap, which leads to a radio phase lag of ~0.13 prior to the first Delta *g-ray peak.