Using a data sample of 6.8 pb$^{-1}$ collected with the CMD-3 detector at the VEPP-2000 $e^+e^-$ collider we select about 2700 events of the $e^+e^- \to p\bar{p}$ process and measure its cross section at 12 energy ponts with about 6\% systematic uncertainty. From the angular distribution of produced nucleons we obtain the ratio $|G_{E}/G_{M}| = 1.49 \pm 0.23 \pm 0.30$.