Abstract: In this paper, the local resonance acoustic metamaterial band structure has been studied with the transfer function, and the recursive method of one−dimensional local resonance periodic structure has been obtained. The mechanism of the band gap formation in a finite metamaterial is determined by the expression of the transfer function. Comparing the finite acoustic metamaterial dynamics analysis with the infinite−length metamaterial Bloch theorem, it is shown that the correctness of the bandgap can be calculated by the transfer function method, and the band−effect of the system pole can be generated and changed by the transfer function method when it comes to the number of primitive cells to control the band gap range.