The Weibull distribution is widely employed in several areas of engineering because it is an extremely flexible distribution with different shapes. Moreover, it can include characteristics of several other distributions. However, successful usage of Weibull distribution depends on estimation accuracy for three parameters of scale, shape and location. This issue shifts the attentions to the requirement for effective methods of Weibull parameters estimation. It is a known fact that the estimation procedure is inherently a very complicated procedure when the three-parameter Weibull distribution is of interest. Hence, this study suggests a computational approach, Greedy randomized adaptive Search procedures, with several neighborhood local Searches to enhance the quality of estimations. Computational experiments are also implemented to assess the quality of estimations as opposed to benchmark grid Search algorithm.