In　this　paper,　we　consider　the　single-index　measurement　error　model　with　mismeasured　covariates　in　the　nonparametric　part.　To　solve　the　problem,　we　develop　a　simulation-extrapolation　(SIMEX)　algorithm　based　on　the　local　linear　smoother　and　the　estimating　equation.　For　the　proposed　SIMEX　estimation,　it　is　not　needed　to　assume　the　distribution　of　the　unobserved　covariate.　We　transform　the　boundary　of　a　unit　ball　in　Rp　to　the　interior　of　a　unit　ball　in　Rp-1　by　using　the　constraint　=1.　The　proposed　SIMEX　estimator　of　the　index　parameter　is　shown　to　be　asymptotically　normal　under　some　regularity　conditions.　We　also　derive　the　asymptotic　bias　and　variance　of　the　estimator　of　the　unknown　link　function.　Finally,　the　performance　of　the　proposed　method　is　examined　by　simulation　studies　and　is　illustrated　by　a　real　data　example.