AN Cam is a little-studied eclipsing binary containing somewhat evolved components in an orbit with a period of 21.0 d and an eccentricity of 0.47. A spectroscopic orbit based on photoelectric radial velocities was published in 1977. AN Cam has been observed using the TESS satellite in three sectors: the data were obtained in long-cadence mode and cover nine eclipses. By modelling these data and published radial velocities we obtain masses of 1.380 +/- 0.021 Msun and 1.402 +/- 0.025 Msun, and radii of 2.159 +/- 0.012 Rsun and 2.646 +/- 0.014 Rsun. We also derive a precise orbital ephemeris from these data and recent times of minimum light, but find that the older times of minimum light cannot be fitted assuming a constant orbital period. This could be caused by astrophysical or instrumental effects; forthcoming TESS observations will help the investigation of this issue. We use the Gaia EDR3 parallax and optical/infrared apparent magnitudes to measure effective temperatures of 6050 +/- 150 K and 5750 +/- 150 K: the primary star is hotter but smaller and less massive than its companion. A comparison with theoretical models indicates that the system has an approximately solar chemical composition and an age of 3.3 Gyr. Despite the similarity of their masses the two stars are in different evolutionary states: the primary is near the end of its main-sequence lifetime and the secondary is now a subgiant. AN Cam is a promising candidate for constraining the strength of convective core overshooting in 1.4 Msun stars.
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