•The effect of eccentricity on the threshold capture velocity of droplets with fiber is studied.•Increasing eccentricity decreases the threshold capture velocity.•The analytical solution considering the surface wettability is presented.•The analytical model can estimate the threshold velocity with fair accuracy.•The hydrophobic fibers may only capture the small droplets in a central impact. The experimental study and volume of fluid numerical simulation are performed to study the capturing mechanism of liquid droplets in fibrous filters. The study is done by focusing on the single droplet impact on a horizontal fiber. In the meantime, analytical expression based on the energy balance method incorporating the effect of variation of wall adhesion and droplet eccentricity is developed for the threshold capture velocity of the droplet. The comparison of experimental results with the analytical expression shows a better agreement than the previous analytical methods where the effects of variation of wall adhesion and droplet eccentricity were not taken into account. The results of our study show that increasing the eccentricity and the ratio of droplet radius to fiber radius result in decreasing the threshold velocity of droplet capture with hydrophilic fibers. In the case of hydrophobic fibers with receding angle over 90°, the droplet capture is only observed for the central impact of small droplets.