Resistance and magnetic torque measurements have been performed for a two dimensional organic superconductor λ-(BETS)2GaCl4, where BETS stands for bis(ethylenedithio)tetraselenafulvalene. In magnetic fields along the c-axis (parallel to the conducting layers), the interlayer resistance shows a peak at ∼7 T for large currents in the superconducting state. The peak disappears when the magnetic field is tilted from the layers only by 0.2°, which shows that the peak is caused by the dynamics of the Josephson vortices penetrating in the insulating layers. The currentvoltage characteristics show that the depinning current of the Josephson vortices is consistently suppressed at around 7 T. The diamagnetic signal, irreversibility field, and depinning current rapidly decrease with increasing field above ∼10 T at low temperatures. The results suggest that there exists a phase boundary in the superconducting state, likely a transition to a Fulde-Ferrell-Larkin-Ovchinnikov phase.