The present invention aims to provide a light-diffusing heat shrinkable tube which has light diffusibility that enables LED point light sources to give an impression of a surface light source such as a conventional fluorescent lamp. The tube is also capable of suppressing scattering of broken fragments of a transparent pipe that includes the light sources, in the case of an unexpected accident including falling of the pipe. The present invention also aims to provide a linear LED light including the light-diffusing heat shrinkable tube. The light-diffusing heat shrinkable tube including a polyester resin and a light diffusing agent, the polyester resin having an inherent viscosity of 0.8 to 1.4 dl/g, the tube comprising 0.1 to 2.5 wt% of the light diffusing agent, the tube having a thickness of 60 to 300 µm.