In electrolytes, the charge carriers are ions, atoms that have gained electrons so they are negatively charged are called anions, atoms that have lost electrons so they are positively charged are called cations. Thus, ions are charged particles (e.g. Na+ sodium ion or Cl- chloride ion in NaCl solution) and their movement or flow constitutes an electric current, i.e. the electrolyte consists of a stream of moving charged particles.
Hence, in electrolytes, current is carried by both + ve and - ve ions.