This　paper　proposes　a　semi-parametric　spatial　lag　quantile　regression　model,　which　can　simultaneously　examine　the　spatial　correlation　of　the　dependent　variables　and　the　partial　nonlinearity　of　the　influencing　mechanism,　and　can　model　the　response　function　at　any　quantile.　Secondly,　the　paper　constructs　a　Bayesian　estimation　method　for　the　model.　In　the　construction　of　the　Bayesian　theoretical　framework,　the　paper　uses　polynomial　splines　to　fit　the　unknown　nonparametric　functions,　and　samples　all　parameters　by　combining　reversible　jump　markov　chain　monte　carlo　(RJMCMC)　algorithm,　random　walk　Metropolis　sampler　and　Gibbs　sampling　technique.　Then　the　accuracy　of　parameter　estimation,　the　fitting　effect　of　unknown　function　and　the　effect　of　practical　application　are　investigated　by　numerical　simulation　method　and　application　example.　The　results　show　that　the　accuracy　of　parameter　estimates　at　three　different　quantile　is　higher　under　two　different　spatial　data　structures　and　a　variety　of　different　sample　sizes.　And　the　fitting　effect　of　non-parametric　unknown　functions　is　good.　The　practical　application　of　the　theoretical　method　is　also　demonstrated.　The　results　of　this　paper　demonstrate　that　the　proposed　model　and　its　theoretical　approach　can　provide　a　powerful　analytical　tool　for　variables　and　data　with　both　linear　and　nonlinear　relationships,　and　with　thick　tails　and　spatial　dependencies.　©　2024　Systems　Engineering　Society　of　China.　All　rights　reserved.