$Bi_6Mg_2Nb_4O_{21}(BMN)$ thin films were deposited at various substrates by sputtering system for embedded capacitor applications. BMN thin films deposited at room temperature are manufactured as MIM(Metal/Insulator/Metal) structures. Dielectric properties and leakage current density were investigated as a function of various substrates and thickness of BMN thin films. Leakage current density of BMN thin films deposited on CCL(Copper Clad Laminates) showed relatively high value ($1{ imes}10^{-3}A/cm^2$) at an applied field of 300 kV/cm on substrates, possibly due to relatively high value of roughness(rms $50{AA}$) of CCL substrates. 100 nm-thick BMN thin films deposited on Cu/Ti/Si substrates showed the capacitance density of $300 nF/cm^2$, a dielectric constant of 32, a dielectric loss of 2 % at 100 kHz and the leakage current density of $1{ imes}10^{-6}A/cm^2$ at an applied field of 300 kV/cm. BMN capacitors are expected to be promising candidates as embedded capacitors for printed circuit board(PCB).