A three-dimensional LED structure with vertically displaced active-region includes at least two groups of vertically displaced surfaces on a non-planar substrate. The first group of surfaces are separated from the second group of surfaces by a vertical distance in the growth direction of the LED structure. The first group of surfaces are connected to the second group of surfaces by sidewalls, respectively. The sidewalls can be inclined or vertical and have a sufficient height so that a layer such as an n-type layer, an active-region, or a p-type layer in a first LED structure deposited on the first group of surfaces and a corresponding layer such as an n-type layer, an active-region, or a p-type layer in a second LED structure deposited on the second group of surfaces are separated by the sidewalls. The two groups of surfaces may be vertically displaced from each other in certain areas of an LED chip, while merge into an integral surface in other areas. A method for fabricating the three-dimensional LED structure is also provided.