Inspired by a new compilation of strong-lensing systems, which consist of 204 points in the redshift range 0.0625<z_l_<0.958 for the lens and 0.196<z_s_<3.595 for the source, we constrain three models that generate a late cosmic acceleration: the {omega}-cold dark matter model, the Chevallier-Polarski-Linder, and the Jassal-Bagla-Padmanabhan parametrizations. Our compilation contains only those systems with early-type galaxies acting as lenses, with spectroscopically measured stellar velocity dispersions, estimated Einstein radius, and both the lens and source redshifts. We assume an axially symmetric mass distribution in the lens equation, using a correction to alleviate differences between the measured velocity dispersion ({sigma}) and the dark matter halo velocity dispersion ({sigma}_DM_) as well as other systematic errors that may affect the measurements. We have considered different subsamples to constrain the cosmological parameters of each model. Additionally, we generate a mock data of SLS to asses the impact of the chosen mass profile on the accuracy of Einstein radius estimation. Our results show that cosmological constraints are very sensitive to the selected data: Some cases show convergence problems in the estimation of cosmological parameters (e.g. systems with observed distance ratio D^obs^<0.5), others show high values for the {chi}^2^ function (e.g. systems with a lens equation D^obs^>1 or high velocity dispersion {sigma}>276km/s). However, we obtained a fiduciary sample with 143 systems, which improves the constraints on each tested cosmological model.