  We present the multiply phased current carrying vortex solutions in the U(1)
gauge theory coupled to an $(N+1)$-component SU(N+1) scalar multiplet in the
Bogomolny limit. Our vortex solutions correspond to the static vortex dressed
with traveling waves along the axis of symmetry. What is notable in our vortex
solutions is that the frequencies of traveling waves in each component of the
scalar field can have different values. The energy of the static vortex is
proportional to the topological charge of $CP^N$ model in the BPS limit, and
the multiple phase of the vortex supplies additional energy contribution which
is proportional to the Noether charge associated to the remaining symmetry.
