In this talk we are interested in solutions whose vorticities are large and concentrated uniformly near a smooth curve $ Gamma(t) $ embedded in an infinite cylinder. This type of solutions, vortex filaments, are classical objects of fluid dynamics. Under suitable assumptions it is known to some extent that the curve evolves by its binormal flow. Two special kinds of binormal flows are traveling circle and rotating-translating helix. Solutions concentrating near a traveling circle is called vortex ring which have been studied extensively. In this talk, we will present existence of solutions near rotating-translating helix. The general case is called vortex filament conjecture which is still a well-known open problem. This talk is based on a joint paper with Wan Jie at Beijing University of Technology.