The non-hydrophobically associating water-soluble polymer (DPAM) of acrylamide (AM) and dimethylamino propyl methacrylamide (DMAPMA) was synthesized. Then pH-switchable and CO2-switchable viscoelastic liquids based on DPAM and anionic surfactant sodium dodecyl sulfate (SDS)(referred to as DPAM-SDS) were developed. When minor HCl aqueous solution was added into the DPAM and SDS aqueous mixture or CO2 was bubbled into it, the tertiary amine groups of DPAM were protonated to form quaternary ammonium groups, some of which in the same quaternary ammonium groups of DPAM "bridged" some SDS through noncovalent electrostatic attraction, behaving like a pseudo-hydrophobically associating water-soluble polymer and forming viscoelastic fluids as checked through environmental scanning electron microscope(ESEM) and rheology. Upon removing of CO2 or back of pH by minor NaOH aqueous solution, the quaternary ammonium species of DPAM were deprotonated back to tertiary amine groups, separating the pseudo-hydrophobically associating water-soluble polymer back to DPAM and SDS molecules, which resulted in forming low-viscosity water solution. The switchable viscoelastic conversion can be repeated.