This letter investigates movable antenna (MA)-aided downlink (DL) multiuser communication systems under the near-field channel condition, where both the base station (BS) and the users are equipped with MAs to fully exploit the degrees of freedom (DoFs) in antenna position optimization. We develop a general channel model to accurately describe the channel characteristics in the near-field region and formulate an MA-position optimization problem to minimize the BS's transmit power subject to users' individual rate constraints. To solve this problem, we propose a two-loop dynamic neighborhood pruning particle swarm optimization (DNPPSO) algorithm that significantly reduces the computational complexity as compared to the standard particle swarm optimization (PSO) algorithm while achieving similar performance. Simulation results validate the effectiveness and advantages of the proposed scheme in power-saving for near-field multiuser communications.