We carried out a 3D fully kinetic simulation of Earth's magnetotail magnetic reconnection to study the dynamics of energetic particles. We developed and implemented a new relativistic particle mover in iPIC3D, an implicit Particle-in-Cell code, to correctly model the dynamics of energetic particles. Before the onset of magnetic reconnection, energetic electrons are found localized close to current sheet and accelerated by lower hybrid drift instability. During magnetic reconnection, energetic particles are found in the reconnection region along the x-line and in the separatrices region. The energetic electrons are first present in localized stripes of the separatrices and finally cover all the separatrix surfaces. Along the separatrices, regions with strong electron deceleration are found. In the reconnection region, two categories of electron trajectory are identified. First, part of the electrons are trapped in the reconnection region, bouncing a few times between the outflow jets. Second, part of the electrons pass the reconnection region without being trapped. Different from electrons, energetic ions are localized on the reconnection fronts of the outflow jets.