To improve the resource utilization and satisfy more users, a Greedy Double Auction Mechanism(GDAM) is proposed to allocate resources in grid environments. GDAM trades resources at discriminatory price instead of uniform price, reflecting the variance in requirements for profits and quantities. Moreover, GDAM applies different auction rules to different cases, over-demand, over-supply and equilibrium of demand and supply. As a new mechanism for grid resource allocation, GDAM is proved to be strategy-proof, economically efficient, weakly budgetbalanced and individual rational. Simulation results also confirm that GDAM outperforms the traditional one on both the total trade amount and the user satisfaction percentage, specially as more users are involved in the auction market.