High dielectric constant and its dependence on structural strain and grain boundaries (GB) in La0.7Sr0.3MnO3 (LSMO) thin films are reported. X-ray diffraction, magnetization, and magneto-transport measurements of the LSMO films, made by pulsed laser deposition on two different substrates—MgO and SrTiO3 (STO), were compared to co-relate magnetic properties with dielectric properties. At room temperature, in the ferromagnetic phase of LSMO, a high dielectric constant (6 × 104) was observed up to 100 kHz frequency for the films on MgO, with polycrystalline properties and more high-angle GB related defects, while for the films on STO, with single-crystalline properties but strained unit cells, high dielectric constant (≈104) was observed until 1 MHz frequency. Also, a large dielectric relaxation time with significant broadening from the Debye single-dielectric relaxation model has been observed in samples with higher GB defects. Impedance spectroscopy further shows that large dielectric constant of the single-crystalline, strained LSMO film is intrinsic in nature while that in the polycrystalline films are mainly extrinsic due to higher amount of GBs. The presence of high dielectric constant value until high frequency range rules out the possibility of “apparent giant dielectric constant” arising from the sample-electrode interface. Coexistence of ferromagnetism and high dielectric constant can be very useful for different microelectronic applications.