Auxetic fabrics have gained an increasing attention in the auxetic material area in recent years. Especially, auxetic fabrics fabricated based on both weft-knitted and warp-knitted structures have made some important progress. However, all the knitted auxetic fabrics reported so far are fabricated based on 2D knitted structures, although some of the weft-knitted auxetic fabrics are finally formed into 3D forms. This paper reports a novel kind of 3D auxetic fabric fabricated based on a warp-knitted spacer structure with adoption of a special geometrical configuration which is formed with parallelograms. The auxetic behavior of these fabrics is discussed in terms of tensile direction, geometrical parameter, and repeated extension. The shape fitting ability on a spherical surface is also demonstrated. The results shows that the 3D auxetic fabrics have auxetic behavior in all the fabric plane directions and the highest auxetic effect is obtained when stretched in the weft direction of the fabric. The 3D auxetic fabrics also display an excellent shape fitting ability, which makes them very attractive for various applications where fitting to the human body's shape is highly required, such as bra cups, protectors for knees and elbows, shoes covers, etc.