A method of composition design for metallic glasses was proposed by using the Calculation of Phase Diagrams (CALPHAD) with the assistance of the topological instability criterion. This methodology was demonstrated in the quick and effective searching of glass-forming regions for Ti-Fe-Si and Ti-Zr-Fe-Si alloys containing no biologically toxic elements, e.g., Ni and Cu. In addition, the Ti-Fe-Si system may promote the glass formation owing to the existence of a deep eutectic at the Ti-rich corner. A self-consistent thermodynamic database was constructed based on the CALPHAD approach. The liquidus projection, isothermal sections, and the enthalpy of mixing were calculated by using the database. On the basis of these calculations coupling with the topological instability "lambda λ criterion," the potential glass-forming alloy compositions in a narrow region were suggested for experimental validation. Thereafter, the isothermal sections of the Ti-Zr-Fe-Si quaternary system were calculated at certain contents of Zr. The designed alloys were prepared by arc-melting and followed by melt-spinning to the ribbon shape. The experimental verifications matched reasonably well with the theoretical calculations. This work offers new insights for predicting glass-forming alloys based on thermodynamic arguments; it shall be of benefit for the exploration of new metallic glasses.