Objective The estimation of parameters and unknown regression functions in partially linear models for longitudinal data was investigated. Methods Considering that model parameters often have certain constraints in some statistical applications a method based on constrained least squares and quadratic smoothing local linear estimation was proposed. This method first utilized profile least squares and the Lagrange multiplier method to obtain constrained profile least squares estimators for parameters and regression functions. Then combined with an improved quadratic smoothing local linear estimation method the final estimation of the model under constraints was obtained. Under certain regularity conditions the asymptotic normality of the constructed parameters and the estimators of the regression function was proved. Meanwhile through numerical simulations the biases standard deviations and mean square errors of parameter components under both constrained and unconstrained situations were obtained. The fitting curves of regression functions under both situations were plotted to verify the effectiveness of the proposed method. Results Simulation results showed that compared with estimators without considering constraints estimators considering constraints had higher estimation accuracy. The fitting curves of regression functions demonstrated good fitting effects further confirming the effectiveness of the proposed estimation method. Conclusion In practical research additional information about parameter components can often be obtained and fully utilizing this information can improve estimation accuracy. Compared with unconstrained estimation methods constrained estimation methods can improve estimation efficiency.