Although XQuery is a statically typed, functional query language for XML data, some of its features such as upward and horizontal XPath axes are typed imprecisely. The main reason is that while the XQuery data model allows us to navigate upwards and between siblings from a given XML node, the type model, e.g., regular tree types, can describe only the subtree structure of the given node. Recently, Castagna et al. (2015) and Genevès and Gesbert (2015) independently propose a precise forward type inference system for XQuery using an extended type language that can describe not only a given XML node but also its context. In this paper, as a complementary method to forward type inference systems, we propose a novel backward type inference system for XQuery, using the type language proposed by Genevès and Gesbert (2015). Our backward type inference system provides an exact typing result for XPath axes and a sound typing result for XQuery expressions.