  Applying the distance sum rule in strong gravitational lensing (SGL) and type
Ia supernova (SN Ia) observations, one can provide an interesting cosmological
model-independent method to determine the cosmic curvature parameter
$\Omega_k$. In this paper, with the newly compiled data sets including 161
galactic-scale SGL systems and 1048 SN Ia data, we place constraints on
$\Omega_k$ within the framework of three types of lens models extensively used
in SGL studies. Moreover, to investigate the effect of different mass lens
samples on the results, we divide the SGL sample into three sub-samples based
on the center velocity dispersion of intervening galaxies. In the singular
isothermal sphere (SIS) and extended power-law lens models, a flat universe is
supported with the uncertainty about 0.2, while a closed universe is preferred
in the power-law lens model. We find that the choice of lens models and the
classification of SGL data actually can influence the constraints on $\Omega_k$
significantly.
