This study investigates a linear $ f(T) $ cosmological model to explore late-time cosmic acceleration using observational data. The model incorporates a constant term, allowing the Hubble parameter to be expressed as a function of cosmic redshift for non-relativistic pressureless matter. The analysis uses 31 data points from the Cosmic Chronometer (CC) dataset, 1048 points from the Pantheon SNe Ia samples, and 6 points from the BAO dataset. The best-fit values for the Hubble constant $ H_0 $, and model parameters $ \alpha $ and $ \beta $ are determined, showing a stable model capable of explaining late-time cosmic acceleration without requiring a dark energy component. The results indicate $ H_0 = 67.8_{-1.3}^{+1.3} $ km/s/Mpc, $ \alpha = -0.99891_{-0.00016}^{+0.00017} $, and $ \beta = -20.1_{-1.9}^{+2.0} $. The model's behavior aligns with the $ \Lambda $ CDM model, showing an increasing Hubble parameter with redshift and a transition from decelerated to accelerated expansion at $ z_t = 0.60 $. The energy density of dark energy decreases over time, and the equation of state parameter $ \omega_{DE} $ is found to be $ -0.68 $, consistent with quintessence. Stability analysis using scalar perturbations confirms the model's robustness, with perturbations decaying over time. The study demonstrates that the $ f(T) $ model can effectively explain late-time cosmic acceleration without invoking dark energy.This study investigates a linear $ f(T) $ cosmological model to explore late-time cosmic acceleration using observational data. The model incorporates a constant term, allowing the Hubble parameter to be expressed as a function of cosmic redshift for non-relativistic pressureless matter. The analysis uses 31 data points from the Cosmic Chronometer (CC) dataset, 1048 points from the Pantheon SNe Ia samples, and 6 points from the BAO dataset. The best-fit values for the Hubble constant $ H_0 $, and model parameters $ \alpha $ and $ \beta $ are determined, showing a stable model capable of explaining late-time cosmic acceleration without requiring a dark energy component. The results indicate $ H_0 = 67.8_{-1.3}^{+1.3} $ km/s/Mpc, $ \alpha = -0.99891_{-0.00016}^{+0.00017} $, and $ \beta = -20.1_{-1.9}^{+2.0} $. The model's behavior aligns with the $ \Lambda $ CDM model, showing an increasing Hubble parameter with redshift and a transition from decelerated to accelerated expansion at $ z_t = 0.60 $. The energy density of dark energy decreases over time, and the equation of state parameter $ \omega_{DE} $ is found to be $ -0.68 $, consistent with quintessence. Stability analysis using scalar perturbations confirms the model's robustness, with perturbations decaying over time. The study demonstrates that the $ f(T) $ model can effectively explain late-time cosmic acceleration without invoking dark energy.