We are concerned with ground-state solutions for the following Kirchhoff type equation with critical nonlinearity: \t\t\t{−(ε2a+εb∫R3|∇u|2)Δu+V(x)u=λW(x)|u|p−2u+|u|4uin R3,u>0,u∈H1(R3),\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\textstyle\\begin{cases} - ({\\varepsilon^{2}}a + \\varepsilon b\\int_{{\\mathbb{R}^{3}}} {{{ \\vert {\\nabla u} \\vert }^{2}}} )\\Delta u + V(x)u = \\lambda W(x){ \\vert u \\vert ^{p - 2}}u + { \\vert u \\vert ^{4}}u\\quad {\\text{in }}{\\mathbb{R}^{3}} ,\\\\ u > 0, \\quad\\quad u \\in{H^{1}}({\\mathbb{R}^{3}}) , \\end{cases} $$\\end{document} where ε is a small positive parameter, a,b>0, lambda > 0, 2 < p le4, V and W are two potentials. Under proper assumptions, we prove that, for varepsilon > 0 sufficiently small, the above problem has a positive ground-state solution {u_{varepsilon}} by using a monotonicity trick and a new version of global compactness lemma. Moreover, we use another global compactness method due to Gui (Commun. Partial Differ. Equ. 21:787-820, 1996) to show that {u_{varepsilon}} is concentrated around a set which is related to the set where the potential V(x) attains its global minima or the set where the potential W(x) attains its global maxima as varepsilon to0.