An additional magnetization damping for an inhomogeneous spin texture in metallic ferromagnets is calculated on the basis of the s - d exchange model. The effect of conduction electrons on the magnetization dynamics is accounted for the case of slowly varying spin texture within adiabatic approximation by using a coordinate transformation to the local quantization axis. The moving magnetic vortex in a circular nanodot made of permalloy is considered as an example. The dependence of the damping on the dot geometrical sizes is obtained. It is found that the additional damping can reach up to 50 % of magnitude of the phenomenological Gilbert damping in the Landau - Lifshitz equation of magnetization motion and should be taken into account for any inhomogeneous spin texture dynamics in ferromagnetic metals.

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