Abstract: Background and Objective: Owing to the wide use of Weibull distribution in solar energy analysis, researchers are constantly looking for easy and applicable methods for estimating its parameters with the smallest margin of error. This study was aimed to find a new algorithm that computes the Weibull parameters easily and accurately. Materials and Methods: Weibull distribution was performed to model the daily solar energy and corresponding maximum temperature in Queensland, Australia over a year. A new method, called nested percentiles algorithm was suggested for estimating the parameters. Anderson-Darling test was applied to measure the fitness of the suggested estimator. Results: Nested percentile algorithm gave high significant results as indicated by Anderson-Darling test. The parameters estimated by the new algorithm provided the best fit of the used datasets over than other results produced by EasyFit program. Conclusion: Nested Percentile Algorithm made two-parameter Weibull distribution more accurate than three-parameter distributions such as; modified Weibull distribution. It also gave more accurate results than EasyFit program.