Summary: In this paper, the pointwise properties of locally \(k\)-uniform rotund Orlicz sequence space with the Luxemburg norm are discussed. For the Orlicz sequence spaces generated by a N-function and endowed with the Luxemburg norm, criteria of \(k\)-uniform rotund points on the spherical surface are obtained. As a conclusion, both sufficient and necessary conditions are presented to make them be locally \(k\)-uniform rotund.