A heat pipe with a flexible support structure includes a pipe body and a support, and the support is installed in the pipe body and includes a first row of side plates and a second row of side plates extended along the lengthwise direction of the pipe body and a plurality of support elements coupled between the first and second rows of side plates, and each support element abuts the internal side of a capillary tissue of the pipe body. Plate elements of the first and second rows of side plates are arranged with an interval apart from each other and in sections along the lengthwise direction of the pipe body, and the plate elements of the first row of side plates and the plate elements of the second row of side plates are aligned alternately with each other. The support is flexible to facilitate users to bend the heat pipe.