Axial pipe-soil interaction is crucial for the prediction of pipeline walking, especially on a sloping seabed. In this study, a mechanical-actuator facility has been specially designed and utilized to simulate the axial pipe-soil interactions along a sloping sandy seabed. Based on dimensional analyses, an apparent axial anti-sliding coefficient is proposed to describe the anti-sliding capacity for pipeline walking on a sloping seabed under the fully-drained condition. Effects of the pipeline surface roughness, the submerged weight (G) of the pipeline and the slope angle (alpha) of the seabed on the apparent axial anti-sliding coefficient are investigated experimentally. The experimental results indicate that, for a fixed value of the non-dimensional submerged pipeline weight, both the ultimate anti-sliding capacity and the corresponding mobilization displacement increase with the increase of the slope angle of the seabed. There exist approximately linear correlations between the apparent anti-sliding coefficient and the examined seabed slope angle (- 9 degrees <= alpha <= 9 degrees) or the non-dimensional submerged pipeline weight (0.34 <= G <= 0.81). An expression for the apparent axial anti-sliding coefficient incorporating an updated wedging factor is finally deduced and validated with the present experimental results. This axial pipe-soil interaction model may help assessing the pipeline walking along subsea continental slopes.