Using a first-principles method, we study field emission properties of double-wall carbon nanotubes with various end geometries and combinations of inner and outer walls. The open double-wall nanotubes exhibit substantial contribution to the emission current from the extended π states. These states are insensitive to the detailed tip structure or the presence of foreign adsorbed molecules and the resulting emission current is expected to be stable under moderate vacuum environment. The mechanical stiffness also increases significantly compared to the single-wall nanotube, ensuring prolonged device lifetime under high-field operating conditions of the field emission display.