The temporal stability and growth characteristics of three-dimensional supersonic shear layers are numerically investigated. An explicit time-marching scheme that is second-order accurate in time and fourth-order accurate in space is used to study this problem. The shear layer is excited by instability waves computed from a linear stability analysis and random initial disturbances. At low convective Mach numbers, organized vortical structures develop both for the random disturbance and the modal disturbance cases. At supersonic convective Mach numbers, vortical structures develop initially but are not sustained in time. Temporal growth of disturbances is found to be a strong function of the convective Mach number.