Surface magnetic domains of a UCoGa single crystal during magnetization/demagnetization processes in increasing/decreasing magnetic fields were investigated by means of magnetic-force-microscopy (MFM) images at low temperatures. The observed domain structure is typical for a ferromagnet with strong uniaxial anisotropy. The evolution of magnetic domains during cooling of the crystal below TC has also been manifested by MFM images. Analysis of the available data reveals that the high uniaxial magnetocrystalline energy in combination with the relatively small ferromagnetic exchange interaction in UCoGa gives rise to the formation of very narrow domain walls formed by the pairs of the nearest U neighbor ions with antiparallel magnetic moments within the basal plane. Since the very high anisotropy energy is a common feature of the majority of the uniaxial U ferromagnets, analogous domain-wall properties are expected for all these materials.