We grew a $Li_6Lu(BO_3)_3:Ce^{3+}$ single crystal as a new scintillator. And, the scintillation and thermoluminescence properties of the scintillator were determined. The emission spectrum of $Li_6Lu(BO_3)_3:Ce^{3+}$ is located in the range of 370~530 nm, peaking at 416 nm and 439 nm, due to the $5d{ ightarrow}4f$ transition of $Ce^{3+}$ ions. The fluorescence decay time of the crystal is composed two components. The fast component is 34 ns (84%) and the slow component is 125 ns (16%) of the crystal. The afterglow is caused by the electron and hole traps in the crystal lattice. We determined physical parameters of the traps in the crystal. The thermoluminescence trap are composed a trap. The determined activation energy (E) and frequency factor (s) of the TL trap are 1.05 eV and $4.4{ imes}10^{10}s^{-1}$, respectively.