The present invention provides an electron beam apparatus provided with an electron-emitting device which has a simple structure, shows high electron-emitting efficiency and stably works. This electron beam apparatus has an insulating member and a gate formed on a substrate, a recess portion formed in the insulating member, a protruding portion that protrudes from an edge of the recess portion toward the gate and is provided on an end part of a cathode opposing to the gate, which is arranged on the side face of the insulating member; and makes an electric field converge on an end part in the width direction of the protruding portion to make an electron emitted therefrom.