A new strategy for synthesis of hyperbranched polymers from commercially available A(2) type and BB2' type monomers has been developed. In the first part of this series, hyperbranched polysulfone-amine with multiamino groups is prepared by polyaddition of 1-(2-aminoethyl)piperazine (BB2') to divinyl sulfone (A(2)) without any catalysts. The products are soluble in water and organic solvents such as N,N-dimethylformamide, chloroform, and N-methyl-2-pyrrolidone. The polymerization mechanism has been investigated with FTIR, HPLC, and MS. During the reaction, secondary amino groups of 1-(2-aminoethyl)piperazine react rapidly with vinyl groups of divinyl sulfone within 15 s, forming dominant dimers and some other species. The dimer can be considered as a new AB(2)' type of monomer. Further reactions among AB(2)' molecules and AB(2)' with other species result in the formation of hyperbranched polymers. The degree of branching of the resulting polymer is higher than 50%. No gelation occurs in solution polymerization when the A(2) to BB2' ratio equals 1. Similarly, there is no gelation in solution polymerization if the feed ratio of A(2) to BB2' is 3/2; however, gelation does occur when the resulting polymer is separated from the solution. There are both terminal amino groups and vinyl groups in the hyperbranched polysulfone-amine if the feed A(2) to BB2' ratio is 3/2, which further react with each other in bulk state resulting in a cross-linked material. If the terminal amino groups are protected by hydrochloride acid in advance in the solution, then no gelation can be observed after the product is separated from the solution.