Transmembrane β-barrel (TMB) proteins are a special class of transmembrane proteins which play several key roles in human body and diseases. Due to experimental difficulties, the number of TMB proteins with known structures is very small. Over the years, a number of learning-based methods have been introduced for recognition and structure prediction of TMB proteins. Most of these methods emphasize on homology search rather than any biological or chemical basis. We present a novel graph-theoretic model for classifi- cation and structure prediction of TMB proteins. This model folds proteins based on energy minimization rather than a homology search, avoiding any assumption on availability of training dataset. The ab initio model presented in this paper is the first method to allow for permutations in the structure of transmembrane proteins and provides more structural information than any known algorithm. The model is also able to recognize β-barrels by assessing the pseudo free energy. We assess the structure prediction on 42 proteins gathered from existing databases on experimentally validated TMB proteins. We show that our approach is quite accurate with over 90% F-score on strands and over 74% F-score on residues. The results are comparable to other algorithms suggesting that our pseudo-energy model is close to the actual physical model. We test our classification approach and show that it is able to reject α-helical bundles with 100% accuracy and β-barrel lipocalins with 97% accuracy.