In our studies, we combined two powdered materials, i.e., ferroelectric triglycine sulfate (TGS) and ferrimagnetic magnetite Fe₃O₄, to obtain a magnetoelectric composite. The ferroelectric (E) part, i.e., TGS, was a hybrid organic–inorganic crystal, which we obtained as a pure single crystal from an aqueous solution using a static water evaporation method. The magnetic (M) part of the composite was commercially available magnetite. The samples used for the dielectric and magnetoelectric measurements were cold-pressed and made in the form of a circular tablet. The measuring electrodes were made of silver-based conductive paste and were attached to the sample. We measured the temperature dependencies of selected electrical parameters (e.g., dielectric permittivity, electrical capacity, and loss angle tangent). We used the dynamic lock-in method to check whether magnetoelectric coupling existed between the E and M phases. In this paper, we present the dielectric properties of pure monocrystalline TGS as a reference sample and compare the results for TGS powder, TGS + carbon powder, and TGS + Fe₃O₄ powder. The magnetoelectric coupling presumably appeared for the composite TGS + 10 wt. % Fe₃O₄, as evidenced by the shift in the phase transition temperature in the TGS. Moreover, the theoretical interpretation of the effect is proposed.