The invention is related to an insulated pipe assembly as well as a method for insulating a pipe. To improve the heat insulating properties of the pipe, it is suggested that the insulated pipe assembly comprises: - a first insulation element (3) arranged on the pipe (2) to form an inner insulation layer around the pipe (2), wherein the first insulation element (3) comprises mineral wool; - support means (5) arranged on the pipe (2) and adjacent to the first insulation element (3); - a second insulation element (4) forming an outer insulation layer around the inner insulation layer and arranged on and supported by the support means (5) arranged on the pipe (2) and - adjacent second insulation elements (4) directly abut on each other in axial direction (13) of the pipe with their end faces (12).