We investigate the motions of dust particles in a complex plasma by applying an axisymmetric nonuniform magnetic field, B, introduced with a permanent magnet. The magnetic field changes its direction from upward to downward within the experimental area. The distribution of dust particles is conical in the meridional plane, and its central area is a void. The dust particles are generally stagnant in the vertical direction and distributed in multiple layers. The horizontal plane is separated into two regions where the vertical component of B can and cannot be regarded as zero. The distribution of the dust particles in the horizontal plane is concentric. The dust particles along the inner and outer edges rotate in opposite directions due to the direction of the vertical component of B and generate shear flow at a certain height. The rotation velocities of the particles at the edges are compared with the theory of Kaw et al. [Phys. Plasmas 9, 387 (2002)]. The vortex-like structure is not easy to observe even in the presence of a shear flow because of the influence of the other dust particles as well as the small Reynolds number of the dust fluid.