As for the robust parameter design of functional responses, a Bayesian Seemingly Unrelated Regression (SUR) model is proposed to take into account the model uncertainty and response variability in this paper. First of all, the SUR model is used to build the functional relationship between the output responses and the input factors at different time points. Also, Bayesian analysis of the SUR model is performed to consider the influence of the model parameter uncertainty on the research results. Secondly, the process means and variances of the functional responses at different time points are estimated by the posterior samples of the simulated responses. Moreover, an integrated performance index (i.e. mean square error) is establish by using the above process means and variances. Then, the optimal parameter settings may be found by minimizing the MSE performance index. Finally, the advantages of the proposed method are illustrated by an example from the literature.