We report on a simple design for a multi-GHz tunable-repetition-rate diode-pumped picosecond laser. Using a plano-Brewster Nd:GdVO4 crystal in a V-folded cavity employing only readily available commercial components, we achieved passive mode-locking with 4.4-ps pulses tunable in the range 2.5-2.7 GHz. This laser is meant to be employed in the MIR experiment that aims at the detection of the Schwinger radiation (dynamical Casimir effect).