b-metric spaces are a kind of generalized metric spaces，which have attracted extensive attention of scholars at home and abroad in recent years. In this paper，the convex structure is firstly introduced in b-metric spaces，and consequently the notion of the convex b-metric space is shown. Moreover，Mann iteration is proposed in above space. Furthermore，by utilizing the sequence which is generated by Mann iteration，under some conditions，it is proved that contractive mappings have the unique fixed point in the complete convex b-metric spaces respectively.