12 strong-motion stations are selected and based on 584 seismic records recorded during the 2010-2012 Canterbury earthquake sequences, New Zealand, a systematic variability analysis of the deep-soft site response (SAF, i.e., site amplification function) in Christchurch city area is conducted with a reference outcropping station LPCC. Thereafter, influence factors including ground motion intensity roughly measured by PGA, magnitude Mw, hypocentral distance Rhypo and azimuths on the variability of SAF are analyzed. The results show that: 1) ground motion intensity PGA has weak effect on mean lg(SAF) values except that PGA tends to strengthen amplification effect for long period components; while under different PGA subdividing bins, the standard deviations of lg(SAF) for bins with PGA greater than 0.6m/s2 are considerably larger than those for PGA less than 0.6m/s2 bins, indicating possible subsoil non-linearity tends to increase the site response variability; 2) seismic magnitude shows little influence on the variability of site response and the means and standard deviations of log10(SAF) for different Mw dividing bins demonstrate similar patterns; 3) hypocentral distance is an another important influence factor on site response variability, that is, the variability of SAF with Rhypo less than 5km is larger than that with Rhypo were larger than 5km; 4) the variability of SAF is basically independent of source azimuths to stations which means the uncertainty of SAF remains closely similar in different azimuth bins.