Objective To study the spatial correlation of response variables in functional data according to existing research methods functional data with spatial dependence were studied and the Bayesian estimation method was proposed. Methods Based on the typical spatial autoregressive model and according to the spatial dependence of the functional response variables the spatial function autoregressive model was generated by assuming that there was an endogenous relationship between the response variables and the explanatory variables. The functional components in the model were changed into discrete types by the principal component analysis and then the complete conditional posterior distribution of the parameters in the calculation model was calculated under a given prior condition. The parameters in the model were estimated using the Bayesian MCMC method. Results The Metropolis-Hastings algorithm which combined Gibbs sampling and random walk was used to estimate the parameters in the model. Through simulation research it was found that the functional coefficients of the model and the estimation deviations and mean square errors of other parameters under different parameter models were small which verified the effectiveness of the Bayesian estimation method. At the same time the spatial function model was applied to the empirical analysis of the average price of new houses in the main urban area of Chongqing. The results show that the Bayesian estimation method of the proposed model is effective. Conclusion The estimation effect of functional explanatory variables using Bayesian estimation method to estimate the parameters in the model is always better under different circumstances and its estimation effect is also more and more effective as the sample size increases. Thus it can be considered that using spatial function model to estimate the spatial function autoregressive model is effective and feasible. Meanwhile the empirical analysis shows that the average house price of new houses in the main urban area of Chongqing has spatial autocorrelation and it will be affected by the listing volume of second-hand houses.