  The {\it crossing number} of a graph $G$ is the minimum number of pairwise
intersections of edges in a drawing of $G$. Motivated by the recent work
[Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper
bound on the crossing number of the hypercube. J. Graph Theory {\bf 59},
145--161 (2008)] which solves the upper bound conjecture on the crossing number
of $n$-dimensional hypercube proposed by Erd\H{o}s and Guy, we give upper and
lower bounds of the crossing number of locally twisted cube, which is one of
variants of hypercube.
