This　article　considers　statistical　inference　for　restricted　semiparametric　varying-coefficient　spatial　autoregressive(SVCSAR)　models.　We　propose　a　restricted　estimation　method　for　parametric　and　nonparametric　components,　and　a　Lagrange-multiplier-type　test　for　testing　hypotheses　on　the　parametric　component　restrictions　of　SVCSAR　models.　Under　mild　conditions,　we　obtain　the　asymptotic　normality　for　the　resulting　estimator　of　the　parametric　vector　and　the　optimal　convergence　rate　for　that　of　nonparametric　functions.　Simulation　studies　are　carried　out　to　investigate　the　finite　sample　performance　of　the　proposed　method.　The　method　is　exemplified　with　Boston　housing　price　data.