An LED replacement-lamp design concept comprising tapered waveguides to provide uniform and broad light distribution is disclosed. Currently, most LED-based replacement lamps for tubular fluorescent lamps place discrete surface-mount LEDs directly on a cylindrical base, which produce wasteful, non-uniform and directional illumination unsuitable for large space and high-ceiling applications. An LED lamp design, proposed as a tubular lamp replacement, comprises of a plurality of discrete LEDs mounted on a common substrate, where all light from each LED is immediately guided and broadened through a tapered waveguide long enough to seamlessly terminate at the lamp's semi-circularly curved cover surface. Many such LED-waveguide assemblies can fill the entire curved cover with diffused and uniform light distribution, resulting in illumination over broad angular ranges. The proposed lamp has a “D” shaped cross-section wherein the lamp's flat side is used as a heat-sink base to be placed against the ceiling or some blocking surface.