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IM Per is a detached A7 eccentric eclipsing binary star. We have obtained extensive measurements of the light curve (28,225 differential magnitude observations) and radial velocity curve (81 spectroscopic observations) which allow us to fit orbits and determine the absolute properties of the components very accurately: masses of 1.7831 ± 0.0094 and 1.7741 ± 0.0097 solar masses, and radii of 2.409 ± 0.018 and 2.366 ± 0.017 solar radii. The orbital period is 2.25422694(15) days and the eccentricity is 0.0473(26). A faint third component was detected in the analysis of the light curves, and also directly observed in the spectra. The observed rate of apsidal motion is consistent with theory (U = 151.4 ± 8.4 year). We determine a distance to the system of 566 ± 46 pc.