Soliton dynamics is studied in a discrete magnetic nano-dot chain by means of micromagnetic simulations together with an analytic model equation. A soliton under a dissipative system is driven by an applied field. The field-driven dissipative soliton enhances its mobility nonlinearly, as the characteristic frequency and the intrinsic Gilbert damping decrease. During the propagation, the soliton emits spin waves which act as an extrinsic damping channel. The characteristic frequency, the maximum velocity, and the localization length of the soliton are found to be proportional to the threshold field, the threshold velocity, and the initial mobility, respectively.