At present, most researches on gas-liquid two-phase flow use a power-law fluid model. However, with the development of unconventional petroleum resources and the restarting of heavy oil, the fluid showed strong yield characteristics. The power-law constitutive will not be able to express the yield-pseudoplastic fluid rheological properties. In order to make the study applicable to a larger range of shear rates, this study used the Herschel-Bulkley fluid model to discuss the gas-liquid flow characteristics. Based on the Herschel-Bulkley fluid constitutive, a two-fluid model, combined with dimensionless and iterative calculation methods, was used to theoretically derive the prediction model of liquid holdup and pressure drop for gas-liquid stratified flow. The effects of non-Newtonian fluid rheological parameters, flow conditions, and pipeline geometry on Herschel-Bulkley fluid and gas stratified flow were further analyzed. The results show that the power-law index n and the yield stress tau(0) (characterizing the rheological characteristics of the liquid phase) have significant effects on the gas-liquid two-phase stratified flow. Specifically, the enhanced liquid yield and shear thinning characteristics will lead to an increase in liquid holdup and a decrease in pressure drop. Comparing with the experimental data, the calculation model proposed in this work has a good prediction effect and provides new insights into the flow behavior of gas and waxy heavy oil with yield stress.