Real-time three dimensional simulations of the electrical tree initiation process in needle-plane geometry under DC field with practical parameters were conducted. The evolution of physical parameters in this dynamic process was presented. Three governing equations: the continuity equation, the transport equation and the Poisson equation, were used to describe charge injection and motion, and an iteration simulation method was proposed to characterize the reciprocal effect of electron injection and local field modification. During the simulation, the transferred energy was regarded as thermal energy, which diffuses and causes local temperature to increase. When a local temperature exceeds the pre-set threshold, partial thermal breakdown occurs, indicating electrical tree initiation. The temperature evolutions of the point right below the needle tip with time under different voltages reflect an apparent deterministic feature of the electrical tree initiation process.