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The Wiener polarity index (usually denoted by Wp) of an alkane is the number of unordered pairs of carbon atoms which are separated by three carbon–carbon bonds. This topological index Wp is useful for predicting the boiling points of alkanes. Deng [MATCH Commun. Math. Comput. Chem. 66 (2011) 305] proved that the maximum Wp value among all alkanes, with n carbon atoms, is 3n-15. The main purpose of present paper is to find all those alkanes with n carbon atoms, which attain the maximum value of Wp. [ABSTRACT FROM AUTHOR]