A single electrically conducting droplet falling through a non-uniform horizontal magnetic field is numerically investigated. Its dynamic behaviors, such as the decrease in the falling velocity, the deformation of the shape, and the flow fields inside the droplet are discussed. Within the numerical framework, the Volume-of-Fluid interface tracking method coupling with an adaptive mesh refinement technique is utilized, while a consistent and conservative scheme is applied for the calculation of the induced electromagnetic field. Basically, it is found that if the droplet keeps spherical shape during the translating, the magnetohydrodynamic effects are identical whether the nonuniform magnetic field is linearly increased or linearly decreased along the falling direction of the droplet, and the numerical results are in good agreement with the analytical solutions. However, in most of the cases that the droplet deformations can not be ignored, their shapes evolve into two categories: being prolate or oblate depended on the direction of the magnetic field gradient. Besides, the aspect ratio of the droplet and the deceleration of its falling velocity are also related to three factors: the initial velocity of the droplet, the gradient and the global strength of the magnetic fields. In addition, we find the internal flows inside the droplet to be rather important in affecting the droplet motion, which is not reported before. Moreover, sometimes we observe the shape of the droplet to oscillate after exiting the non-uniform magnetic field, complying with an oscillatory mode 2. After that, we consider other circumstance by adjusting the inclination between the magnetic field and the gravitational direction, finding the trajectory of the droplet to deviate from the rectilinear path, and the evolutions of the vortex structures at the tail of the droplet are presented when the inclined angle is varied. (C) 2018 Elsevier Ltd. All rights reserved.