Abstract We analyze the time and energy dependence of the Vela pulsar’s pulse profile using 13 yr observations from the Large Area Telescope on the Fermi Gamma-ray Space Telescope. It is found that the pulse profile of the Vela pulsar in γ-ray changes with time. We parameterize the pulse profile and find that different shape parameters show fluctuations rather than gradual changes with time. However, these time variation trends are insignificant due to limited statistics. The pulse profile of the Vela pulsar displays clear energy dependence in γ-ray. Different shape parameters are accurately obtained or updated, especially the phase separations among different pulses. Their energy evolution trends are quantified for the first time, which will provide restrictions on current γ-ray emission models. For the Vela pulsar, we also find a turning point at phase. Before and after this phase, the relative intensity of the pulse profile evolves with energy with the opposite trend.

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