Precisely controllable, defect-free neutral atom arrays have emerged as an outstanding platform for exploring complex quantum many-body systems and advancing quantum simulation and quantum computing. A method that boosts the rapid and efficient rearrangement is of great significance for expanding the scale of atomic arrays. Here, we present a fast parallel atomic array assembly method based on a PPM algorithm, i.e., position matching, path planning, and move in parallel. By optimizing atom-to-target trajectories using reduced position matching and introducing trajectory correction and target exchange in path planning, the PPM method can effectively minimize movement steps and displacement. The simulation of assembling atoms in parallel into arbitrary geometries shows a reduction of 49% and 35% in steps and displacement compared with the previous parallel algorithm, respectively. Our PPM simulation demonstrates the achievement of a defect-free arrangement of 1,024 atoms in only 35 steps.