A mathematical model was derived in this study to reveal the mechanism of CO₂ imbibition in shale formations considering the combined effects of capillary force and viscous force in concave curved triangle pore channels surrounded by different solid materials with different wettability. The model reveals that CO₂ imbibition depth is proportional to the square root of CO₂ soaking time, square root of the pore size determined by grain size, square root of interfacial tension and cosine of contact angle, and inversely proportional to the square root of CO₂ viscosity. Up to three solid wall materials with different contact angles can be considered in the model. Using the average contact angle for the three materials over-estimates the imbibition distance. CO₂ imbibition is faster in concave curved triangle pores than in equivalent circular-shaped pores. The dimensionless geometry correction factor is less than unity $(\alpha =0.81)$. The newly developed imbibition model can be used for predicting the maximum time of imbibition between parallel fractures in multi-fractured shale formations.