We continue our work (Y. Li, C. Zhao, Locating the peaks of least-energy solutions to a quasilinear elliptic Neumann problem, J. Math. Anal. Appl. 336 (2007) 1368–1383) to study the shape of least-energy solutions to the quasilinear problem εmΔmu−um−1+f(u)=0 with homogeneous Neumann boundary condition. In this paper we focus on the case 1+, the global maximum point Pε of least-energy solutions goes to a point on the boundary ∂Ω at a rate of o(ε) and this point on the boundary approaches a global maximum point of mean curvature of ∂Ω.