We have devised a practical approach for the synthesis of aliphatic polysulfones by the strategy of group transfer radical polymerization. This protocol employs new butenylsulfone and pentenylsulfone monomers, avoids the use of gaseous SO2, generates a diverse array of ABC sequence-defined aliphatic polysulfones with high molecular weights and low distributions. DFT calculations have been performed and reveal that a radical Smiles rearrangement pathway is involved in the GTRP process.