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We study the ground-state phases of two-dimensional rotating spin-orbit coupled spin-1/2 Bose-Einstein condensates (BECs) in a gradient magnetic field.The competition between gradient magnetic field,spin-orbit coupling and rotation leads to a variety of ground-state phase structures.In the weakly rotation regime,as the increase of gradient magnetic field strength,the BECs experiences a phase transition from the unstable phase to the single vortex-line phase.The unstable phase presents the vortex lines structures along the off-diagonal direction.With magnetic field gradient strength increasing,the number of vortex lines changes accordingly.As the magnetic field gradient strength increases further,the single vortex-line phase with a single vortex line along the diagonal direction is formed.The phase diagram shows that the boundary between the two phases is linear with the relative repulsion λ ≥ 1 and is nonlinear with λ ＜ 1.In the relatively strong rotation regime,in addition to the unstable phase and the single vortexline phase,the vortex-ring phase is formed for the strong magnetic field gradient and rapid rotation.The vortex-ring phase shows the giant and hidden vortex structures at the center of ring.The strong magnetic field gradient makes the number of the vortices around the ring unchanged.