A detailed study of the g-factor anisotropy of electrons and holes in InAs/In0.53Al0.24Ga0.23As selfassembled quantum dots emitting in the telecom spectral range of 1.5−1.6 µm (around 0.8 eV photon energy) is performed by time-resolved pump-probe ellipticity technique using a superconducting vector magnet. All components of the g-factor tensors are measured, including their spread in the quantum dot (QD) ensemble. Surprisingly, the electron g factor shows a large anisotropy changing from ge,x = −1.63 to ge,z = −2.52 between directions perpendicular and parallel to the dot growth axis, respectively, at an energy of 0.82 eV. The hole g-factor anisotropy at this energy is even stronger: |g h,x | = 0.64 and |g h,z | = 2.29. On the other hand, the in-plane anisotropies of electron and hole g factors are small. The pronounced out-of-plane anisotropy is also observed for the spread of the g factors, determined from the spin dephasing time. The hole longitudinal g factors are described with a theoretical model that allows us to estimate the QD parameters. We find that the QD height-to-diameter ratio increases while the indium composition decreases with increasing QD emission energy.