Degradable fiber is widely used to assist gelled acid diversion and reduce acid leak-off in the acid stimulation of carbonate hydrocarbon reservoirs in Sichuan Basin of China. The rheological properties of an acid system will affect the geometry of the acid-etching fracture. However, the effect of fiber on the rheological properties of gelled acid is not yet clear. This paper investigates the rheological properties of gelled acid with various fiber concentrations at different temperatures. The results show that when the temperature is less than the degradable temperature of the fiber, the apparent viscosity of gelled acid rises gradually with an increase in fiber concentration, while the fiber has no significant effect on the viscosity of gelled acid at the degradable temperature. The dissolution process of fiber in gelled acid experiences none-dissolution, surface dissolution, dissolution and fining, and a complete dissolution stage from low to high temperatures, which all have different effects on gelled acid viscosity. The fiber links more gelling agent molecules of gelled acid together to form a quasi-network structure between the fiber and fiber and the fiber and polymer, which results in a rise in the viscosity of gelled acid. The acid system also shows a strong shear thinning property under different temperatures and fiber concentrations. However, the power-law index n of this acid system always maintains a steady average value of about 0.181, while the change pattern of consistency index K is similar to the change in viscosity with varying fiber concentrations and temperatures. The research results are useful for acid fracturing treatment design in carbonate reservoir.