A new tungsten single-crystal target has been successfully employed at the positron source of the KEKB injector linac. The crystal thickness was determined to be 10.5 mm based on previous systematic measurements of the positron-production efficiency. The crystal axis, ⟨111⟩, was precisely aligned to the direction of the 4-GeV primary electron beam. The positron yield increased by ∼25% compared to that for a conventional tungsten plate with a thickness of 14 mm. On the contrary, the steady-state heat load on the crystal target decreased by ∼20%. After a two-month operation, no degradation of the positron-production efficiency was observed, and the crystal target has been stably operating at the KEK B factory.