Summary: This paper focuses on the infinite lattice systems \[ \ddot{q}(n)+f'(q(n))=V'(q(n+1)-q(n))-V'(q(n)-q(n-1)), n\in \mathbb Z, \] where \(q(n)=q(n, t)\) denotes the coordinate of \(n\)-th particle at time \(t\), \(f\) a potential function and \(V\) the potential of interaction between the \(n\)-th and the \((n-1)\)-th particles. The existence of new type periodic travelling wave solutions is established by mountain pass theorem and link theorem.