A Laue lens is an optical component composed of a set of crystals that produce a convergent beam exploiting X-ray diffraction in transmission geometry. Employment of a system formed by a properly designed Laue lens coupled with an X-ray unit to selectively irradiate tumours is proposed. A convergent beam leads to a depth dose profile with a pronounced peak at the focal depth, which may result in a high precision of the dose delivery. Using a custom-made Monte Carlo code and the GAMOS code, we carried out a design study to determine the geometry and the optimal features of the crystals composing the lens. As an application, a Laue lens capable of focusing a 80keV beam 50cm downstream of the lens has been designed. The lens is composed of an ensemble of Si crystals with curved diffracting planes. The lens produces a focal spot of 2mm enclosing 7.64 × 106 photons for an electron charge of 1mC impinging on the surface of the X-ray tube anode. The combination of these important figures of merit makes the proposed system suitable for irradiating both sub-cm and larger tumour masses efficiently. A dose of 2Gy can be delivered to a small tumour in a few seconds, sparing at the same time the surrounding tissues.