To face the challenges lying beyond present technologies based on complementary metal-oxide-semiconductors, new paradigms for information processing are required. Magnonics(1) proposes to use spin waves to carry and process information, in analogy with photonics that relies on light waves, with several advantageous features such as potential operation in the terahertz range and excellent coupling to spintronics(2). Several magnonic analog and digital logic devices(3) have been proposed, and some demonstrated(4). Just as for spintronics, a key issue for magnonics is the large power required to control/write information (conventionally achieved through magnetic fields applied by strip lines, or by spin transfer from large spin-polarized currents). Here we show that in BiFeO3, a room-temperature magnetoelectric material(5), the spin-wave frequency (>600 GHz) can be tuned electrically by over 30%, in a non-volatile way and with virtually no power dissipation. Theoretical calculations indicate that this effect originates from a linear magnetoelectric effect related to spin-orbit coupling induced by the applied electric field. We argue that these properties make BiFeO3 a promising medium for spin-wave generation, conversion and control in future magnonics architectures.