Solid solutions of the (1-x)$BiFeO_3-xSrTiO_3$ ceramic system (x = 0~0.4) are explored here in attempts to obtain multiferroic properties in these systems. The polarization-electric field hysteresis, magnetization-magnetic field curves, and dielectric properties are also characterized. This solid-solution system shows a crystal structural transition from a noncentrosymmetric (R3c) structure to a centrosymmetric (Pm-3m) structure at 0.3 < x < 0.4. The solid solution ceramic shows unsaturated M-H behavior and low remanent magnetization over the composition region of 0.1 ${leq}$ x ${leq}$ 0.3. The $0.7BiFeO_3-0.3SrTiO_3$ system shows the largest value of $M_s$ at 0.17 emu/g and the smallest value of $H_c$ at 1.06 kOe. The P-E hysteresis curves were not saturated under an electric field as high as E = 70 kV/cm. This system is considered to have multiferroic characteristics in the composition range of 0.1 ${leq}$ x ${leq}$ 0.3.