  The Hilbert-Schmidt distance between a mixed three-qubit state and its
closest state is used to quantify the amount of pairwise quantum correlations
in a tripartite system. Analytical expressions of geometric quantum discord are
derived. A particular attention is devoted to two special classes of
three-qubit $X$ states. They include three-qubit states of ${\rm W}$, ${\rm
GHZ}$ and Bell type. We also discuss the monogamy property of geometric quantum
discord in some mixed three-qubit systems.
