  Quantum discord is a manifestation of quantum correlations due to
non-commutativity rather than entanglement. Two measures of quantum discord by
the amount of non-commutativity via the trace norm and the Hilbert-Schmidt norm
respectively are proposed in this paper. These two measures can be calculated
easily for any state with arbitrary dimension. It is shown by several examples
that these measures can reflect the amount of the original quantum discord.
