We are interested in the following critical biharmonic Schrödinger equation \( \left\{ \begin{array}{ll} \Delta ^2 u+\lambda u=g(u)+|u|^{4^*-2}u \,\,\,\, \text{ in }\,\,\, \mathbb {R}^{N}, \\ \int _{\mathbb {R}^N}|u|^2 dx=c, \end{array}\right. \) where \(5\le N\le 7\) , \(4^*:=\frac{2N}{N-4}\) , \(c>0\) and \(\lambda \in \mathbb {R}\) appears as a Lagrange multiplier. The novelty of this paper is that, under a class of general mass-supercritical conditions on g(u), we obtain the existence of ground state solutions and derive an asymptotic behavior of the ground state energy as \(c\rightarrow +\infty \) . The key ingredient of our proof relies on an alternative criterion and some subtle energy estimation technique. Some recent results are generalized and improved significantly.
