Solution stability of parametric variational systems with smooth-boundary constraint sets is investigated. Sufficient conditions for the lower semicontinuity, Lipschitz-like property, and local metric regularity in Robinson΄s sense of the solution map are obtained by using a calculus rule for the normal second-order subdifferential from B.S. Mordukhovich (Variational Analysis and Generalized Differentiation, Vol.I: Basic Theory, Vol.II: Applications, Springer, Berlin, 2006) and the implicit function theorems for multifunctions from G.M. Lee, N.N. Tam and N.D. Yen (J Math Anal Appl 338:11–22, 2008). [ABSTRACT FROM AUTHOR]