UCoAl crystallizes in the ZrNiAl-type hexagonal structure, exhibits a paramagnetic ground state, but a metamagnetic transition to a ferromagnetic state with uranium magnetic moments parallel to the c axis occurs at low temperatures when a field of 1 T is applied in this direction. We present the results of a polarized neutron experiment on a UCoAl single crystal. Experimental data have been analyzed by a maximum entropy method and within an atomic model. The main magnetic contribution originates from the uranium atoms. The ratio μL/μS between the orbital and spin moment is slightly reduced in comparison to the uranium free ion value and remains nearly unchanged between 1 and 8 T. Induced magnetic moments of nearly same magnitude and similar field dependence are observed on the two cobalt sites. An additional magnetization density is observed around the aluminum positions. The results are discussed in context of former studies on isostructural UTX compounds.