A novel deformable rolling mechanism is proposed in this paper. The mechanism can switch between two modes: a planar linkage mode and a spherical linkage mode. In the planar linkage mode, the mechanism rolls like a planar four-bar mechanism and moves along a straight line. In the spherical linkage mode, the mechanism rolls as a spherical four-bar mechanism and moves along a polygon. A standing posture, which likes an upright pyramid, of the rolling mechanism is also identified. After the description of the novel mechanism, the kinematic analysis of the mechanism is presented, and appropriate control strategies are proposed. Then, the rolling conditions of the mechanism are investigated based on the zero-moment-point theory. Finally, the various modes of the mechanism are verified by both simulations and prototype experiments.