Abstract: The estimator of extreme value index is one of the important research topics in extreme value statistics. This paper focuses on the estimator of a positive extreme value index. Firstly, with the help of two statistics, four estimators of the positive extreme value index with the parameter α are proposed. The consistency and asymptotic normality of the proposed estimators are proved under the first-order regular variation condition and the second-order regular variation condition. Further, the four estimators become asymptotical unbiased by choosing appropriate parameter. Secondly, the performance of the new estimators in terms of asymptotic properties and finite sample properties is discussed. In terms of asymptotic properties, the new estimators perform better when compared with the existing asymptotical unbiased estimators. In the finite sample, a new method of choosing the parameter α is proposed, and the new estimators are compared with the existing ones through Monte-Carlo simulations. The results show that the proposed method of selecting the parameter α is feasible and the new estimators perform better. Finally, we propose an idea of constructing asymptotical unbiased estimator of a positive extreme value index.