The magnetic properties of Zn₂TiO₄ single crystals were investigated by physical property measurement system (PPMS). The field dependent magnetization (M-H) curves showed a weak ferromagnetism at low field and diamagnetism at high field for Zn₂TiO₄ single crystals. The zero-field-cooled (ZFC) and field-cooled (FC) curves further confirmed ferromagnetic behavior of the sample. With the temperature decreasing from 300 to 10 K, the weak ferromagnetism increased slowly. Around 50 K, the M-T curves had a shoulder. After the temperature decreased to 10 K, the ferromagnetism increased significantly. The magnetic mechanism was investigated using the first-principle calculations method. The origin of the ferromagnetic was discussed.