An intriguing bipolar mass outflow and a faint envelope were detected spectroscopically in the planetary nebula NGC 6751 by Gieseking and Solf (1986). To study the physical structure, deep CCD images of this nebula have been obtained which detect not only the morphological counterparts of the aforementioned features but also additional faint halos extending out to a much larger radius. Long-slit echelle spectra are obtained to determine the internal motion and radial velocity, as well as 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. An He abundance difference between the planetary nebula and the ambient medium and an N/O abundance ratio enhancement in the forbidden N II-bright knots in the main nebula are found. From the physical structure of the shells in NGC 6751, information is derived about the average mass-loss rates at various stages.