An intriguing bipolar mass outflow and a faint envelope were detected spectroscopically in the planetary nebula NGC 6751 by Gieseking & Solf To study the physical structure, we have obtained deep CCD images of this nebula, which detect not only the morphological counterparts of the aforementioned features but also additional faint halos extending out to a much larger radius. We have further obtained long-slit echelle spectra to determine the internal motion and radial velocity, and low-dispersion spectra to determine the physical condition and abundances of each feature in the whole nebula. NGC 6751 is apparently a multiple-shell nebula moving through a gas-rich environment. We find an He abundance difference between the planetary nebula and the ambient medium; we also find an N/O abundance ratio enhancement in the [N II]-bright knots in the main nebula. From the physical structure of the shells in NGC 6751 we derive information about the average mass-loss rates at various sta s.