Let A be a p-variate Wishart matrix on n degrees of freedom with identity co variance.The distributions of extreme eigenvalues of A have important applications in multivariate statistics.Consider the asymptotics when p grows in proportion to n, it is known from existing work that after centering and scaling, these distributions approach the orthogonal Tracy-Widom law for real and unitary Tracy-Widom law for complex valued data, both of which can be numerically evaluated and tabulated in software.Under the same assumption, we show that a carefully chosen transformation improves the accuracy of the Tracy-Widom limit to second order: O(min(n, p)(-2/3)).The accuracy results are valid for both complex and real valued data.Together with the numerical simulation, it implies that the Tracy-Widom law is an attractive approximation to the distributions of these extreme eigenvalues, which is important for using the approximation in practice.