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Canonical ensemble Monte Carlo simulations have been carried out to investigate the thermodynamic properties of two-dimensional fluids subjected to truncated Lennard-Jones 12-6 potential. The simulations of thermodynamic states sweep across liquid-vapor regime over a wide range of thermodynamic conditions. Simulated isotherms behave van der Waals loop-like characteristics in the liquid-vapor phase-transition region. It suggests a continuous isothermal phase transition in the case of micro system, in which the system size prohibits phase separation. Two-dimensional dimensionless van der Waals equation of states has been obtained from theoretical analysis. By fitting simulated data to this equation, temperature-dependent parameters in the equation have been determined.