The　penalized　variable　selection　methods　are　often　used　to　select　the　relevant　covariates　and　estimate　the　unknown　regression　coefficients　simultaneously,　but　these　existing　methods　may　fail　to　be　consistent　for　the　setting　with　highly　correlated　covariates.　In　this　paper,　the　semi-standard　partial　covariance　(SPAC)　method　with　Lasso　penalty　is　proposed　to　study　the　generalized　linear　model　with　highly　correlated　covariates,　and　the　consistencies　of　the　estimation　and　variable　selection　are　shown　in　high-dimensional　settings　under　some　regularity　conditions.　Some　simulation　studies　and　an　analysis　of　colon　tumor　dataset　are　carried　out　to　show　that　the　proposed　method　performs　better　in　addressing　highly　correlated　problem　than　the　traditional　penalized　variable　selection　methods.　©　Springer-Verlag　GmbH　Germany　&　The　Editorial　Office　of　AMS　2024.