The adhesive contact between a half-space with a single surface micro-groove and a flat half-space is investigated. Surface interaction is described by the Maugis-Dugdale adhesion model. The contact problem is reduced to a singular integral equation for a height of the interface gap, which is solved analytically. For evaluating widths of the gap and the adhesion zone, a system of two transcendental equations is obtained, which is solved numerically. Three stable equilibrium states are found. The gap width-applied pressure curves are characterized by discontinuities and hysteresis. The effects of the maximum groove height and the adhesive stress on the adhesive contact are studied. It is shown that the adhesion hysteresis is greater for smaller grooves and larger adhesive stresses.