Plant leaves, insects and geckos are masters of adhesion or anti-adhesion by smartly designed refined surface structures with micro- and nano- technologies. Understanding the basicprinciples in the design of the unique surface structures is of great importance in the manufacture or synthesis of micro- and nano- devices in MEMS or NEMS. This study is right inspired by this effort, focusing on the mechanics of wet adhesion between fibers having concave tips and a fiat substrate via capillary forces. We show that the concave surface can effectively enhance the wet adhesion by reducing the effective contact angle of the fiber, firmly pinning the liquid bridge at its circumferential edge. A critical contact angle is identified below which the adhesion strength can achieve its maximum, being insensitive to the contact angle between the fiber and liquid. The analytical expression for the critical angle is derived. Then a tentative design for the profile of concave surfaces is proposed, considering the effects of chamfering size, deformation and buckling,etc. The effect of liquid volume on the wet adhesion of multiple-fiber system is also discussed.