Here, we report the exfoliation of bulk MoS2 (molybdenum disulfide) into few-layer nanosheets and then prepared nanocomposite films with poly(ethylene oxide) (MoS2-PEO). We observed nonpolar or polarity independent bistable resistive switching memory in two-terminal devices with indium tin oxide (ITO) and aluminum (Al) as bottom and top electrodes, respectively. In both bipolar and unipolar operation, it is observed that the biasing direction controls the current conduction mechanism. When positive bias is applied at the top Al electrode, the low resistance state (LRS) conduction is ohmic type. But in opposite biasing condition, LRS conduction is space charge controlled. The current-voltage characteristics of the bipolar and unipolar switching are distinctly different in terms of their RESET process. In bipolar, the RESET process is very sharp whereas in unipolar operation it is staggered and step-wise.