An air pump includes a body being composed of two semi-housings. A sleeve is received in an opening at a top of the body. A rim is formed at a top of the sleeve and an annular recess is defined at a bottom of the sleeve. By fasteners through the rim, the sleeve is secured in the body. A motor is mounted on the body for driving a gear assembly in the body. A piston has a movable block movably received in the sleeve and a linkage eccentrically connected to the gear assembly. A discharge valve with a nozzle is mounted on the sleeve for discharging compressed air out from the nozzle. Whereby, the sleeve can be made with a small thickness, so its cost is low. Moreover, it is easy to install the sleeve in the correct position to ensure the piston to smoothly reciprocate in the sleeve.