A novel zwitterionic monomer 3-[(2-acrylamido)dimethylammonio]propanesulfonate (DMADAS) was designed and synthesized in this study. Then it was polymerized with acrylamide (AM) by free radical polymerization in 0.5 mol/L NaCl solution with ammonium persulfate ($(NH_4)_2S_2O_8$) and sodium sulfate ($NaHSO_3$) as initiator. The structure and composition of DMADAS and acrylamide-3-[(2-acrylamido)-dimethylammonio]propanesulfonate copolymer (P-AM-DMADAS) were characterized by FT-IR spectroscopy, $^1H$ NMR and elemental analyses. Isoelectric point (IEP) of P-AM-DMADAS was tested by nanoparticle size and potential analyzer. Solution properties of copolymer were studied by reduced viscosity. Antipolyelectrolyte behavior was observed and was found to be enhanced with increasing DMADAS content in copolymer. The results showed that the viscosity of P-AM-DMADAS is 5.472 dl/g in pure water. Electrolyte was added, which weakened the mutual attraction between sulfonic acid group and quaternary ammonium group. The conformation became loose, which led to the increase of reduced viscosity. The ability of monovalent and divalent cation influencing the viscosity of zwitterionic copolymer obeyed the following sequence: $Li^+$ < $Na^+$ < $K^+$, $Mg^{2+}$ < $Ca^{2+}$ < $Ba^{2+}$, and that of anion is in the order: $Cl^-$ < $Br^-$ < $I^-$, $CO{_3}^{2-}$ > $SO{_3}^{2-}{approx}SO{_4}^{2-}$.