The double perovskite La2FeMn1−xCuxO6 ((x = 0.1, 0.2, 0.3, 0.4 and 0.5) was synthesized by using conventional solid-state reaction method. The crystal structure of the double perovskite was confirmed to be orthorhombic (Pnma) by Rietveld refinement of the powder X-ray diffraction. The average grain sizes of the prepared samples were calculated to be in the range of 0.5–1 µm. Energy dispersive x-ray spectroscopy confirmed the presence of La, Fe, Mn, Cu and O in the samples. Jahn-Teller distortion plays a crucial role in the structural distortion of the system. Due to the ionic radii mismatch of the B-site substituents, an extra Raman mode was identified for substituted systems. The frequency dependence of dielectric, AC conductivity and impedance spectroscopy were investigated at different temperatures within the frequency range 10 Hz to 1 MHz. We observe a Maxwell-Wagner type of polarization in the variation of the dielectric constant. A non-Debye relaxation behaviour was observed in the Nyquist plot. From the behaviour of frequency exponent with temperature, the conduction mechanism was described by the Correlated Barrier Hopping model (CBH).