<p>Partial linear model (PLM) integrates parametric and nonparametric regression model, which more closely aligns with real-world scenarios and has more flexibility. To address the estimation issues within this model, in this paper, we first employ a Kernel estimation method to estimate the nonparametric components, then translate the PLM to a linear regression model. Ordinary least squares (LS) estimation in linear regression is highly sensitive to high-variance errors, particularly under heavy-tailed distributions or outliers. To enhance robustness while addressing the sparsity of coefficients along with their sequential disparities, we construct a least absolute deviation (LAD) model with fused lasso penalty (LAD-Flasso) to estimate parameters, which yields a robust estimator capable of simultaneously achieving estimation and variable selection. Then we analyze the near-oracle property of the LAD-Flasso estimator and design a semi-proximal alternating direction method of multipliers (sPADMM) to solve the LAD-Flasso. Finally, we demonstrate the robustness of the LAD-Flasso model and the effectiveness of our proposed algorithm through numerical experiments on simulated and real-world data.</p>