A three-dimensional (3D) highly-directive emission system is proposed to enable beam shaping and beam steering capabilities in wideband frequencies. It is composed of an omnidirectional source antenna and several 3D gradient-refractive-index (GRIN) lenses. To engineer a broadband impedance match, the design method for these 3D lenses is established under the scenario of free-space excitation by using a planar printed monopole. For realizations and demonstrations, a kind of GRIN metamaterial is proposed, which is constructed by non-uniform fractal geometries. Due to the non-resonant and deep-subwavelength features of the fractal elements, the resulting 3D GRIN metamaterial lenses have extra wide bandwidth (3 to 7.5 GHz), and are capable of manipulating electromagnetic wavefronts accurately, advancing the state of the art of available GRIN lenses. The proposal for the versatile highly-directive emissions has been confirmed by simulations and measurements, showing that not only the number of beams can be arbitrarily tailored but also the beam directions can be steerable. The proposal opens a new way to control broadband highly-directive emissions with pre-designed directions, promising great potentials in modern wireless communication systems.