Here we study the spin-1 particle, i.e., an electromagnetic wave in curved spacetime, say, around a black hole. After separating the equations into radial and angular parts and writing them according to a black-hole geometry, e.g. a Kerr black hole, we solve them analytically. Finally, we produce a complete solution of the spin-1 particles around a rotating black hole, i.e., in Kerr geometry. Obviously there is coupling between the spin of the electromagnetic wave and that of the black hole when particles propagate in that spacetime. Thus, the solution will be dependent on the coupling strength. Most importantly, it may be useful in studying other different problems where analytical results are needed. The results may also be useful in some astrophysical contexts.