Infrared (IR) laser-line scanning has been widely used to induce different surface microstructures in a broad range of materials. In this work, this laser configuration was applied on the surface of MgTi0.06B2 bulk samples in order to ascertain its effects on their superconducting properties, particularly on the magnetic levitation forces. The microstructural changes produced by this type of laser treatment were investigated by X-ray diffraction (XRD) and Scanning Electron Microscopy (SEM). It was observed that the thermal treatment induced by the laser improves grain connectivity in a layer of material just below the irradiated surface, in agreement with the observed improvement in critical current density values, J(c), which were estimated from isothermal magnetic hysteresis loops. A significant increment of both vertical (F-z) and lateral (F-x) magnetic levitation forces was achieved. Numerical calculations were performed to understand the experimental behaviour and to clarify how an improvement of J(c) near the surface can improve the magnetic levitation force of these materials. In addition, the same studies were carried out in similar bulk samples but with nano-sized silver particle additions of 3 and 6 wt %, in the outer ring of the bulk, observing also an improvement of the levitation forces, albeit less than in samples without Ag because of the better performance of the original samples after laser treatment. These results are relevant to those studying superconductor fabrication and material fabrication modelling, essential for the development of technological applications of superconductors, and are based on microstructure control via application of a recently developed laser-line scan method. (C) 2019 Elsevier B.V. All rights reserved.