The effects of Nb and Co ion substitution on the dielectric and magnetic properties of the multiferroic $BiFeO_3$ thin films have been investigated. Heteroepitaxial $BiFeO_3$ thin films were deposited by Pulsed Laser Deposition method. Nb substitution decreased the leakage current by 6 orders of magnitude and Co substituted $BiFeO_3$ thin films showed an enhanced magnetization, 2 times larger than that of un-substituted $BiFeO_3$. Through the co-substitution of Co and Nb, $BiFeO_3$ thin films with a low leakage current and an enhanced magnetization could be obtained.