To improve the efficiency and durability of a trochoid gear pump by reducing sliding resistance of an outer gear against a pump casing.

Vane grooves 38 for increasing pressure are formed in the outer periphery of the outer gear 25, and the inner periphery of the pump casing 23 for storing the outer gear 25 is provided with a pressure introducing port 39 for introducing fluid to the vane grooves 38 of the outer gear 25 and a pressure releasing port 40 for releasing fluid pressure increased in the vane grooves 38 by rotation of the outer gear 25. The pressure introducing port 39 and the pressure releasing port 40 are positioned so that an unbalanced load acting on the outer periphery of the outer gear 25 due to the fluid pressure increased in the vane grooves 38 of the outer gear 25 acts in a substantially opposite direction of an unbalanced load acting on the inner periphery of the outer gear 25 due to the fluid pressure increased in a pump chamber 30 between both gears 25 and 26, and the number and sizes of the vane grooves 38 are set so that both unbalanced loads have the substantially the same size.