Subsurface images based on low-fold seismic reflection data or data with geometry acquisition limitations, such as obtained from ocean-bottom seismography (OBS), are often corrupted by migration swing artifacts. Incorporating prestack instantaneous slowness information into the imaging condition can significantly reduce these migration swing artifacts and improve image quality, especially for areas with poor illumination. We combine the horizontal surface slowness information of observed seismic data with Gaussian-beam depth migration to implement a new slowness-driven Gaussian-beam prestack depth migration whereby Fresnel weighting is combined naturally with beam summation. The prestack instantaneous slowness information is extracted from the original OBS or shot gathers using local slant stacks and is combined with a local semblance analysis. During migration, we propagate the seismic energy downward, knowing its instantaneous slowness information. At each image location, the beam summation is localized in a resolution-dependent Fresnel zone; the instantaneous slowness information controls the beam summation. Synthetic and real data examples confirm that slowness-driven Gaussian-beam migration can suppress most noise from inadequate stacking and give a clearer migration result.