From the 2002 data taking with a neutral kaon beam extracted from the CERN-SPS, the NA48/1 experiment observed 97 $Xi^{0}rightarrow Sigma^{+} mu^{-} bar{ u}_{mu}$ candidates with a background contamination of $30.8 pm 4.2$ events. From this sample, the BR($Xi^{0}rightarrow Sigma^{+} mu^{-} bar{ u}_{mu}$) is measured to be $(2.17 pm 0.32_{mathrm{stat}}pm 0.17_{mathrm{syst}})times10^{-6}$.