AgNbO3 is a weak ferroelectric with antiferroelectricity due to Ag displacements at room temperature. A dielectric anomaly at 250K, which has not been observed previously, reveals a transition between the weak ferroelectric phase (M1 phase) at the higher temperature and a new ferroelectric phase (M0 phase) at the lower temperature in AgNbO3. This transition was further verified by the pyroelectric current and differential scanning calorimetry measurements. The spontaneous polarization value is found to be much larger in the M0 phase than that of the M1 phase. A well-defined saturating ferroelectric hysteresis loop can also be observed at 77K, showing a remnant polarization value of 2.4C/cm2 and a coercive field of 25kV/cm. All the above results indicate that the larger polarization of the M0 phase mainly comes from the alignment of the antiferroelectric displacements of the Ag atoms.