The structure and phase transition of a two-dimensional (2D) dusty plasma have been investigated in detail bymolecular dynamics simulation. Pair correlation function, static structure factor, mean square displacement, and bondangle correlation function have been calculated to characterize the structural properties. The variation of intealenergy, shear modulus, particle trajectories and structural properties with temperature has been monitored to studythe phase transition of the 2D dusty plasma system. The simulation results are in favour of a two-step continuoustransition for this kind of plasma.