The voltage-current (V-I) characteristics in superconducting monolayer FeSe film on SrTiO3 (100) under different magnetic fields are investigated. The zero-fieldV-I result exhibits signatures of a Berezinski-Kosterlitz-Thouless transition, a characteristic of two-dimensional (2D) superconductors. Under an applied magnetic field, with current density lower than the critical current density, the sheet resistance versus current density (Rsq-J) dependence changes from ohmic (Rsq independent of J) to non-ohmic (a nonlinear dependence of Rsq on J) as the temperature decreases, indicative of a vortex phase transition/crossover. We interpret the high-temperature phase as the vortex liquid phase and the low-temperature phase as the vortex slush phase, which has short-ranged vortex lattice correlation, while long-range correlation (i.e. true superconductivity) is absent. No transition into a vortex glass phase is seen, illustrating the importance of thermal fluctuations in a perfect 2D superconductor under a magnetic field. © 2016 IOP Publishing Ltd.