Recent X-ray study of middle-aged supernova remnants (SNRs) reveals strong radiative recombination continua (RRCs) associated with overionized plasmas, of which the origin still remains uncertain. We report our discovery of an RRC in the middle-aged SNR 3C 391. If the X-ray spectrum is fitted with a two-temperature plasma model in collisional ionization equilibrium (CIE), residuals of Si XIV Ly alpha line at 2.006 keV, S XVI Ly alpha line at 2.623 keV and the edge of RRC of Si XIII at 2.666 keV are found. The X-ray spectrum is better described by a composite model consisting of a CIE plasma and a recombining plasma (RP). The abundance pattern suggests that the RP is associated to the ejecta from a core-collapse supernova with a progenitor star of 15 solar mass. There is no significant difference of the recombining plasma parameters between the southeast region and the northwest region surrounded by dense molecular clouds. We also find a hint of Fe I K alpha line at 6.4 keV (~2.4 sigma detection) from the southeast region of the SNR.