The recent discovery of superconductivity coexisting with weak itinerant ferromagnetism in the d-electron intermetallic compound ZrZn2 strongly suggests spin-fluctuation mediated superconductivity. Ab initio electronic structure calculations of the Fermi surface and generalized susceptibilities are performed to investigate the viability of longitudinal spin-fluctuation-induced spin-triplet superconductivity in the ferromagnetic state. The critical temperature is estimated to be of the order of 1 K. Additionally, it is shown that in spite of a strong electron-phonon coupling, conventional s-wave superconductivity is inhibited by the presence of strong spin fluctuations.