We present the results of our study of the close pre-main sequence spectroscopic binary CVSO 104 in Ori OB1, based on data obtained within the PENELLOPE legacy program. We derive, for the first time, the orbital elements of the system and the stellar parameters of the two components. The system is composed of two early M-type stars and has an orbital period of about five days and a mass ratio of 0.92, but contrary to expectations, it does not appear to have a tertiary companion. Both components have been (quasi-)synchronized, but the orbit is still very eccentric. The spectral energy distribution clearly displays a significant infrared excess that is compatible with a circumbinary disk. The analysis of He I and Balmer line profiles, after the removal of the composite photospheric spectrum, reveals that both components are accreting at a similar level. We also observe excess emission in Hα and Hβ, which appears redshifted or blueshifted by more than 100 km s−1 with respect to the mass center of the system, depending on the orbital phase. This additional emission could be connected with accretion structures, such as funnels of matter from the circumbinary disk. We also analyze the optical companion located at about 2.″4 from the spectroscopic binary. This companion, which we named CVSO 104 B, turns out to be a background Sun-like star that is not physically associated with the PMS system and does not belong to Ori OB1.