A focusing structure of field-emission arrays (FEAs) made of a parallel planar emitter, gate, and in-plane lens is suggested. Using the particle-in-cell simulation code MAGIC, the diamond-film FEAs made of a strip planar emitter, a parallel gate, and an anode with and without an in-plane lens have been simulated. The electron-beam streamlines and the x-p(y). phase show that the in-plane lens focuses the electron beam. For a typical model, the beam width decreases about 1/10 for every cell, and the transverse velocity decreases from +/-5.5 X 10(6) to +/-0.4 X 10(6) m/s when including the in-plane lens. This structure can be used as a moderated field-emission cathode to emit a collimated electron beam, such as in field-emission displays.