The 2-dimensional angular correlation of the positron annihilation radiation (2D-ACAR) on a single crystal of LaB6 was measured for three projections. The 2D-ACAR spectra were subjected to the Van Citter-Gerhard deconvolution algorithm [1]. The 3-dimensional p-space density rho (p) was reconstructed via the Cormack method [2] and a modified Fourier-transform-based algorithm [3]. The k-space density rho (k) was then obtained by applying the 3D-LCW transformation to rho (p) [4]. Moreover, the Fermi surface was constructed by parameterising its volume with a geometrical model. The geometrical parameters were determined by a least-square fit to the 2-dimensional LCW transformation applied to two high symmetry projections.