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We have grown La$_{1.37}$Sr$_{1.63}$Mn$_2$O$_7$ single crystals with a laser-diode-heated floating-zone furnace and studied the crystallinity, structure, and magnetoresistance (MR) effect by in-house X-ray Laue diffraction, X-ray powder diffraction, and resistance measurements. The La$_{1.37}$Sr$_{1.63}$Mn$_2$O$_7$ single crystal crystallizes into a tetragonal structure with space group \emph{I}4{/}\emph{mmm} at room temperature. At 0 T, the maximum resistance centers around $\sim$166.9 K. Below $\sim$35.8 K, it displays an insulating character with an increase in resistance upon cooling. An applied magnetic field of \emph{B}~=~7~T strongly suppresses the resistance indicative of a negative MR effect. The minimum MR value equals $-$91.23\% at 7 T and 128.7 K. The magnetic-field-dependent resistance shows distinct features at 1.67, 140, and 322 K, from which we calculated the corresponding MR values. At 14 T and 140 K, the colossal negative MR value is down to $-$94.04(5)\%. We schematically fit the MR values with different models for an ideal describing of the interesting features of the MR value versus \emph{B} curves., Comment: 12 pages, 7 figures