Spectroscopy of a $^{10}_{Lambda}$Be hypernucleus was carried out at JLab Hall C using the $(e,e^{prime}K^{+})$ reaction. A new magnetic spectrometer system (SPL+HES+HKS), specifically designed for high resolution hypernuclear spectroscopy, was used to obtain an energy spectrum with a resolution of 0.78 MeV (FWHM). The well-calibrated spectrometer system of the present experiment using the $p(e,e^{prime}K^{+})Lambda,Sigma^{0}$ reactions allowed us to determine the energy levels, and the binding energy of the ground state peak (mixture of 1$^{-}$ and 2$^{-}$ states) was obtained to be B$_{Lambda}$=8.55$pm$0.07(stat.)$pm$0.11(sys.) MeV. The result indicates that the ground state energy is shallower than that of an emulsion study by about 0.5 MeV which provides valuable experimental information on charge symmetry breaking effect in the $Lambda N$ interaction.