We present the first results of directional point-contact spectroscopy in high-quality CaC6 samples both along the ab plane and in the c-axis direction. The superconducting order parameter Delta(0), obtained by fitting the Andreev-reflection (AR) conductance curves at temperatures down to 400 mK with the single-band 3D Blonder-Tinkham-Klapwijk model, presents two different distributions in the two directions of the main current injection, peaked at 1.35 and 1.71 meV, respectively. By ab initio calculations of the AR conductance spectra, we show that the experimental results are in good agreement with the recent predictions of gap anisotropy in CaC6.