In this study, we investigated and compared the hydrolysis resistance properties of three different types of fluoride glasses and their damage characteristics induced by an 800 nm fs (fs) laser. The results show that the hydrolysis resistance of the fluoroaluminate (AYF) glass is significantly higher than that of the fluorozirconate (ZBLAN) and the fluoroindate (IZBS) glass. After soaking in distilled water for 7 days, the average transmittance of the fluoroaluminate glass (AYF) remains around 80% in the range of 2-6 mu m, while that of the other two glasses decrease to zero at the hydroxyl group absorption wavelength of similar to 2.96 mu m. After 24 h of immersion, the mass loss rate of AYF glass is less than one-eleventh of ZBLAN glass and one-eighth of IZBS glass, respectively. Under the irradiation of fs laser (800 nm, 91 fs, 1 kHz), the 1-on-1 mode laser-induced damage threshold of the AYF glass is as high as 5164.9 mJ/cm(2), which is 80.3% higher than that of the IZBS glass (2863.3 mJ/cm(2)) and 16.8% higher than that of the ZBLAN glass (4420.1 mJ/cm(2)). The higher laser damage threshold is attributed to the relative larger optical bandgap and higher Al-F energies of the AYF glass. Using this mechanism, we further tailored the fluoroaluminate glass's optical bandgap increased and the accumulation rate of electrons decreased by introducing up to 20 mol % TeO2 into the AYF glass, finally the fs laser-induced damage threshold of the corresponding sample with 20 mol % TeO2 increased by about 79.5% to the maximum 9272.2 mJ/cm(2), compared with the TeO2-free AYF sample.