The electromagnetic properties of the interface between a left-handed material and a conventional nonlinear material were investigated theoretically and numerically. We found a new phenomenon-optical bistability of the interface.It was shown that the incident intensity, incident angle and permeability ratio between the left-handed and the nonlinear materials could dramatically affect the optical bistable behaviour. We also compared the bistable behaviours of different electromagnetic modes. The results indicated that the TE mode was prior to the TM mode to obtain optical bistability for the same parameter.