We report the discovery of TOI-677.b, first identified as a candidate in light curves obtained within Sectors 9 and 10 of the Transiting Exoplanet Survey Satellite (TESS) mission and confirmed with radial velocities. TOI-677.b has a mass of M-p = 1.236(-0.067)(+0.069) M-J, a radius of R-P = 1.170 +/- 0.03 R-J, and orbits its bright host star (V=.9.8 mag) with an orbital period of 11.23660 +/- 0.00011 d, on an eccentric orbit with e = 0.435 +/- 0.024. The host star has a mass of M-star = 1.181 +/- 0.058 M-circle dot, a radius of R. = 1.28(-0.03)(+0.03) R-circle dot, an age of 2.92(-0.73)(+0.80) Gyr and solar metallicity, properties consistent with a main-sequence late-F star with T-eff = 6295 +/- 77 K. We find evidence in the radial velocity measurements of a secondary long-term signal, which could be due to an outer companion. The TOI-677.b system is a well-suited target for Rossiter-Mclaughlin observations that can constrain migration mechanisms of close-in giant planets.