Single crystals of ferromagnetic UAsSe have been investigated by angle-resolved photoemission spectroscopy (ARPES) in the photon energy range between 20 eV and 110 eV. Electron kinetic energy intensities are collected as a function of angle and mapped onto the materials reciprocal space. Energy-band mapping has been carried out both for a several-eV-wide energy interval as well as for a narrow energy interval of less than 1 eV from the Fermi energy. The main features of the deduced energy bands can be explained by band-structure calculations. In the interval close to the Fermi energy, the very high energy and momentum resolution allows the observation of a narrow, yet dispersive photoemission peak mainly of 5f character situated within 50 meV of the Fermi energy. The Lorentzian linewidth was found to be about 35 meV with a dispersion of 30 meV along the Gamma to Z direction and 40 meV dispersion along the Gamma to X direction in the Brillouin zone. We have also found broader (linewidth about 70 meV), hybridized f-character bands with a conventional dispersion of about 1 eV along the Gamma to X and the Z to R directions in the Brillouin zone. An intriguing electronic structure emerges for UAsSe in which both relatively dispersive and narrow 5f bands are present. The occurrence of 5f-band dispersions stipulates that the electronic structure of UAsSe requires lattice periodicity to be taken into account.