The Windy Postman Problem (WPP), is an interesting generalization of the classical Chinese Postman Problem (CPP), which has many real-world applications. The WPP has been shown to be NP-complete; therefore, it is difficult to solve the problem exactly. For this reason, heuristic solution procedures have been proposed to solve the problem approximately. In this paper, we first review the existing solution procedures, then introduce two new algorithms to solve the WPP near-optimally. Computational results show that the new algorithms outperform the existing solution procedures on some special class of networks.