A linear LED lighting system, assembly and/or fixture distributes luminance efficiently in certain applications, such as for ceiling lighting used in certain retail environments. According to example embodiments of the invention, a linear LED lighting system includes at least two tilted, parabolic reflecting surfaces and a linear array of LED devices, wherein at least some of the LED devices are substantially disposed at a focus line of at least one of the tilted, parabolic reflecting surfaces. A diffuser or diffusive lens can be disposed adjacent to the parabolic reflecting surfaces where light exits the system to provide color mixing and/or eliminate potential hot spots. The tilt of the reflecting surfaces can be changed to adjust the illumination pattern. A lighting system according to example embodiments of the invention can be designed for retrofit installation or as a complete fixture.