Controlled actuation of a floating liquid marble, a liquid droplet coated with hydrophobic particles floating on another liquid surface, is a potential digital microfluidics platform for the transport of aqueous solution with minimal volume loss. This paper reports our recent investigation on the magnetic actuation of floating liquid marbles filled with magnetic particles. The magnetic force and frictional force acting on the floating liquid marble determine the horizontal movement of the marble. We varied the magnetic flux density, flux density gradient, concentration of magnetic particles and speed of the marble to elucidate the relationship between the acting forces. We subsequently determined the suitable operating conditions for the actuation and derived the scaling laws for the actuation parameters.