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This paper discusses a special type of T-spline surfaces called periodic T-splines that are closed in one parameter direction, and their application in tubular surface fitting. First, a global representation is proposed for representing periodic T-splines. This representation does not require repeating control points, which facilitates surface fitting process. Then, an algorithm for adaptively fitting periodic T-splines to a tubular triangular mesh that has the same topology as a cylinder is presented. The resulting periodic T-spline is obtained respecting the geometric distribution of the input mesh. The use of periodic T-splines for tubular surface fitting has at least two advantages: 1) adaptive fitting is easily achieved due to the local refinement of T-splines; 2) the algorithm avoids cutting the mesh to make it a disk topologically for conventional B-spline fitting due to the periodic representation and this overcomes the drawback of finding a good cutting path, which is usually difficult.