  In this article, we investigate the error bound of quantum discord, obtained
by the analytic formula of Ali et al.[Phys. Rev. A 81(2010), 042105] in case of
general X states and by the analytic formula of Fanchini et al.[Phys. Rev. A
81(2010), 052107] in case of symmetric X states. We show that results of Ali
et. al. to general X states and Fanchini et al. to symmetric X states may have
worst-case error of 0.004565 and 0.0009 respectively.
