Two-dimensional (2D) vortex dynamics is studied in YBa2Cu3O7/PrBa2Cu3O7 superlattices by measuring the current-voltage (I-V) characteristics. In the high current limit, the 2D collective creep is observed with an activation energy U(j)proportional toj(-mu), with j the current density. The exponent mu is 0.8 at low temperatures and mu = 0.2 at high temperatures. A dislocation-mediated vortex melting occurs when the temperature is increased. In the low current limit, the exponential growth of the energy barrier for elastic motion is prohibited by the plastic deformation of vortices. The observed plateau in the resistive transition is attributed to the possible quantum tunneling of vortices.