In this paper, the architectural parameters optimization of a three degree-of-freedom (DOF) parallel kinematic machine (PKM) with three PUU (prismatic-universal-universal) links is performed using the efficient particle swarm optimization (PSO) to achieve the best accuracy characteristics. The error transformation matrix (ETM) is derived based on the differentiation of kinematic equations, and the lowest value of the maximum singular value of the ETM over a usable workspace is considered as an error performance index for the optimal design. To emphasize the efficiency of the PSO method, both the traditional direct search method and the genetic algorithm (GA) are compared with it. The simulation results demonstrate that the PSO is the best method for the optimization, and the analysis results are valuable in designing and controlling a 3-PUU PKM for machine tool applications.