Three-parameter Weibull is one of the most popular and most widely-used distribution in many fields of science. Therefore, many studies have been conducted concerning the statistical inferences of the parameters of Weibull distribution. In general, the maximum likelihood (ML) methodology is used in the estimation process of unknown parameters. In this study, the ML estimation of the parameters of Weibull distribution is considered using particle swarm optimization (PSO). As in other heuristic optimization methods, the performance of PSO is affected by initial conditions. The novelty of this study comes from the fact that we propose a new adaptive search space based on confidence intervals in PSO. The modified maximum likelihood (MML) estimators are utilized for constructing the confidence intervals. MML based confidence intervals allow a narrower search space for the parameters of Weibull distribution than the search space used in the literature. Therefore, the performance of PSO increases, since the search space is wisely narrowed. In order to show the performance of the proposed approach, an extensive Monte-Carlo simulation study is conducted. Simulation results show that the proposed approach works well. In addition, real world data is analyzed to show implementation of the proposed method.