A series of water-soluble long branched-chain amphiphilic copolymers, AAGASs, were synthesized and applied in the enhanced oil recovery of heavy oil. Hydrophobically associating water-soluble copolymers (AAGs) with an epoxy group were first synthesized by free-radical copolymerization of acrylamide (AM) and sodium 2-acrylamido-2-methylpropanesulfonic acid with glycidyl methacrylate. An amino-terminated amphiphilic copolymer (AS-N) was also prepared with AM and sodium 4-styrenesulfonate via chain transfer polymerization. AAGASs were then obtained by the chain-extending reaction between the epoxy groups of the AAG and amino group of the AS-N. Fourier transform infrared spectroscopy, H-1 nuclear magnetic resonance spectroscopy, static light scattering, and thermogravimetric analysis measurements were performed to determine the polymer structures and properties. Shear viscosity, surface tension, and interfacial tension were also investigated to understand the oil displacement mechanism of AAGAS solutions. The results showed that AAGASs have a unique associative property in solution and possess good surface and interfacial activities, allowing AAGAS solutions to both thicken water and convert highly viscous heavy oil into low-viscosity oil-in-water emulsions. Measurement of the apparent viscosities showed that AAGAS-3 achieves optimal performance with a degree of viscosity reduction of heavy oil up to 96.8% at 1000 mg/L. Therefore, our work showed a two-pronged approach for enhancing the recovery of heavy oil, namely, using a polymer incorporating water-thickening properties with heavy oil viscosity-reducing ability.