  In this paper, we study the following semilinear Schr\"odinger equation with
periodic coefficient: $$-\triangle u +V(x)u=f(x,u), u\in
H^{1}(\mathbb{R}^{N}).$$ The functional corresponding to this equation
possesses strongly indefinite structure. The nonlinear term $f(x,t)$ satisfies
some superlinear growth conditions and need not be odd or increasing strictly
in $t$. Using a new variational reduction method and a generalized Morse
theory, we proved that this equation has infinitely many geometrically
different solutions. Furthermore, if the solutions of this equation under some
energy level are isolated, then we can show that this equation has infinitely
many $m-$bump solutions for any positive integer $m\geq 2.$
