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Here, we report the growth of (Sr, Ca) Nd2Fe2O7 single crystals with the Ruddlesden–Popper structure using an optical floating-zone method. A significantly anisotropic magneto-dielectric effect (MD), ab-plane and c-axial MD coefficients reaching −12.3% and −8.4% measured at 103 Hz in a 1 T magnetic field, can be obtained in a SrNd2Fe2O7 crystal at room temperature. The corresponding anisotropic MD ratio can be reached as high as 1.46. With an increase in the Ca concentration, the MD effect decreases dramatically and is eventually completely suppressed in both directions. Analysis of magnetic properties and 57Fe Mössbauer spectra suggests that the anisotropic MD effects in SrNd2Fe2O7 can be attributed to polaronic hopping between two neighboring Fe3+ ions through oxygen vacancies in an anisotropically antiferromagnetic matrix; the disappearance of the MD effect in Ca-doped SrNd2Fe2O7 is a consequence of the suppression of the antiferromagnetism. Our work suggests that the significantly anisotropic MD effect in SrNd2Fe2O7 crystals at room temperature can be used in magneto-dielectric controlled devices. [ABSTRACT FROM AUTHOR]