This paper investigates the existence of ground state solutions for the following nonlinear Kirchhoff-type problem \(\begin{aligned} \begin{aligned} \left\{ \begin{array}{ll} -\Bigl (a+b\displaystyle \int _{\mathbb {R}^3}|\nabla u|^2\textrm{d}x\Bigr )\Delta u+\lambda u=f(u) \,\,\,\, \text{ in }\,\,\, \mathbb {R}^3,\\ \displaystyle \int _{\mathbb {R}^3}|u|^2\textrm{d}x=m, \end{array}\right. \end{aligned} \end{aligned}\) where \(a, b>0\) , \(m>0\) is the prescribed mass and \(\lambda \) appears as an unknown Lagrange multiplier. Under a class of reasonable assumptions on f, especially the mixed pure-power nonlinearities \(|u|^{\frac{8}{3}}u+|u|^{p-2}u\) with \(\frac{14}{3}<p<6\) and some other more general nonlinear terms are included, we establish the existence of ground state solutions via employing the constraint minimization technique and making use of minimax arguments involving the homotopy stable family. Recent results related this problem are generalized and improved significantly.
