We demonstrate a current-controlled, dynamic magnonic crystal. It consists of a ferrite film whose internal magnetic field exhibits a periodic, cosine-like variation. The field modulation is created by a direct current flowing through an array of parallel wires placed on top of a spin-wave waveguide. A single, pronounced rejection band in the spin-wave transmission characteristics is formed due to spin-wave scattering from the inhomogeneous magnetic field. With increasing current the rejection band depth and its width increase strongly. The magnonic crystal allows a fast control of its operational characteristics via the applied direct current. Simulations confirm the experimental results. Comment: 4 pages, 3 figures