The design and analysis of a new 7R single-loop multi-mode mechanism (SLMMM) is presented in this paper. The 7R SLMMM is obtained by inserting one R joint into a line and plane symmetric overconstrained Bricard 6R linkage. The new mechanism has three types of operation modes with three different numbers of effective joints including 4R, 6R and 7R modes, while most other SLMMMs only have one or two numbers of effective joints in all operation modes. The kinematic mapping method and the algebraic approach are applied to implement the kinematic analysis of the 7R SLMMM. Motion curves are plotted to illustrate the operation modes and transition configurations. Meanwhile, CAD configurations are presented to verify these motion curves. As a by-product of this work, a new overconstrained 6R mechanism has been identified, which is in fact the proposed 7R mechanism in one of its 6R operation modes.