We report a novel utilization of periodic arrays of carbon nanotubes in the realization of diffractive photonic crystal lenses. Carbon nanotube arrays with nanoscale dimensions (lattice constant 400 nm and tube radius 50 nm) displayed a negative refractive index in the optical regime where the wavelength is of the order of array spacing. A detailed computational analysis of band gaps and optical transmission through the nanotubes based planar, convex and concave shaped lenses was performed. Due to the negative-index these lenses behaved in an opposite fashion compared to their conventional counter parts. A plano-concave lens was established and numerically tested, displaying ultra-small focal length of 1.5 μm (∼2.3 λ) and a near diffraction-limited spot size of 400 nm (∼0.61 λ).