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The evolution of cooperative behaviors of small-world networking agents in a snowdrift game mode is investigated, where two agents (nodes) are connected with probability depending on their spatial Euclidean lattice distance in the power-law form controlled by an exponent α. Extensive numerical simulations indicate that the game dynamics crucially depends on the spatial topological structure of underlying networks with different values of the exponent α. Especially, in the distance-independent case of α=0, the small-world connectivity pattern contributes to an enhancement of cooperation compared with that in regular lattices, even with a high cost-to-benefit ratio r. However, with the increment of α > 0, when r ≥ 0.4, the spatial distance-dependent small-world (SDSW) structure tends to inhibit the evolution of cooperation in the snowdrift game. [ABSTRACT FROM AUTHOR]