Adhesion of solid surfaces plays a significant role in many technical fields especially at micro and nano scale. The effect of asperity shape on the adhesion hysteresis originated from surface roughness has been investigated theoretically in this paper. Based on the adhesive contact model of single asperities with axisymmetric power-law shapes, the roughness-induced adhesion hysteresis is modeled by assuming the asperity heights follow a Gaussian distribution on the rough surface. The analysis results show that the dissipation energy decreases dramatically when the surface becomes rougher for all the shape indices, and the shape index affects the adhesion hysteresis at different levels with the variance of surface roughness. A general parameter consisting of the shape index of asperities is proposed to characterize the adhesion hysteresis. These will be helpful to understand and control the adhesion hysteresis for solid-solid contact.