Summary: The existence of infinitely many solutions for a class of \(p\)-Kirchhoff equations was studied. Assuming that Kirchhoff function \(M\) and weight function \(f\) were weakened, that is \(M\) has no positive lower bound and the sign of \(f\) is indefinite. It is proved that the energy functional \(J\) satisfies the \((PS)_c\) condition by using two important inequalities in \(\mathbb{R}^N\). Moreover, the existence of infinitely many solutions was obtained by Fountain Theorem, and a list of unbounded positive energy solutions was obtained. Thus, the multiplicity result of solution for \(p\)-Kirchhoff equations was extended.