A new kind of dynamo utilizing flowing laboratory plasmas has been identified. The conversion of plasma kinetic energy to magnetic energy is verified numerically by kinematic dynamo simulations for magnetic Reynolds numbers above 210. As opposed to intrinsically-turbulent liquid-sodium dynamos, the proposed plasma dynamo corresponds to laminar flow topology. Modest plasma parameters (1–20 eV temperatures, 1019–1020 m−3 densities in 0.3–1.0 m scale-lengths driven by velocities on the order of the Alfvén critical ionization velocity) self-consistently satisfy the conditions needed for the magnetic field amplication. Growth rates for plasma dynamos are obtained numerically with different geometry and magnetic Reynolds numbers. Magnetic-field-free coaxial plasma guns can be used to sustain the plasma flow and the dynamo.