High precision frequency measurements of ${{}^{127}\text{I}}_2$ hyperfine transitions in the wavelength range between 750 and 780 nm were performed employing an optical frequency comb. A Ti:sapphire laser is frequency stabilized to a hyperfine component of ${\text{I}}_2$ using a Doppler-free frequency modulation technique, and an optical frequency comb is used to measure its frequency precisely. Improved absolute frequencies of 27 hyperfine transitions between 750 and 780 nm of the bands (0–12) and (0–13) of $B{{}^3\Pi }_{0_u^{+}}–X{{}^1\Sigma }_g^{+}$ system of ${\text{I}}_2$ are presented. The relative uncertainty of the measurement is a few times ${10}^{-10}$ , limited by the frequency instability of the iodine-stabilized laser. The frequencies are compared to the predicted frequencies using the model description of [ Eur. Phys. J. D 28, 199 (2004) ], which yields differences larger than expected. An improved model is developed for the range from 755 to 815 nm for the prediction of lines with an error limit of the absolute frequency less than 0.2 MHz.