Understanding the enhanced liquid flow behaviors in nano-scale elliptic pores with different surface wettability has tremendous implications in science and engineering, such as water purification and shale oil recovery with abundant irregular circular (elliptic) pores. In this study, the apparent viscosity and enhancement factor model are proposed considering boundary slip velocity and effective viscosity, which is related to the contact angle, pore dimensions and shapes, and the boundary slip velocity depends on the no-slip Hagen-Poiseille equation depending on near-wall water viscosity. In addition, the proposed model is compared and validated with the results from theories and molecular dynamic simulations. Results show that the apparent viscosity decreases with an increasing contact angle, and tends to bulk viscosity with the increase of pore dimension. With contact angle ranging 0 similar to 180 degrees, the enhancement factor can decrease one order of magnitude with apparent viscosity larger than bulk viscosity, and increase eight orders of magnitude with apparent viscosity smaller than bulk viscosity. With an increasing ratio of semi-long axis a to semi-short axis b of elliptic pores, the apparent viscosity increases first and then decreases down to 0 for a small contact angle, and the enhancement factor decreases first and then increases. In addition, for a larger contact angle, the apparent viscosity gradually decreases and tends to 0, and the enhancement factor increases. The changes of apparent viscosity and enhancement factor are directly related to the changes of boundary velocity and effective viscosity which are caused by the surface wettability, pore dimensions and shapes. The proposed model can be used to describe the liquid flow in nano-scale elliptic pores with different surface wettability, like the shale oil transport in oil-wet organic and water-wet inorganic pores.