Abstract: The class of Nekrasov matrices is one of important subclass of H-matrices,it plays a key role in the research of matrix analysis and numerical algebra.We study bounds of the infinity norm of the inverse of Nekrasov matrices and obtain two new upper bounds which contain a parameter ε.Numerical examples are given to illustrate that the estimates obtained by using the upper bounds are more accurate than that by using some existing upper bounds when the parameter ε is chosen appropriately.