In this paper, a new type of acoustic metamaterial with negative modulus is proposed, and the formation and broadening mechanism of the low frequency bandgap are revealed. The expression of the normalized effective modulus of the structure is derived theoretically. Since the zero value of the effective modulus is closely related to the system parameters, the appropriate parameters can be adjusted to reduce the zero point, and the lower bound of the bandgap is reduced, thus the low-frequency bandgap is realized. The theoretical results show that the elastic modulus of the system is negative and the region of the negative modulus is widened in a certain frequency range, therefore, the widening of the bandgap can be realized through the enlargement of the negative modulus region. This new mechanism for achieving low-frequency bandgap overcomes the shortcomings both in the traditional local resonance with too large additional mass, and in the inertial amplification structures with narrow bandgaps. At the same time, the transmission of this periodic structure obtained by the finite element method is highly consistent with that by the theoretical analysis, with a low-frequency band of 40-180 Hz, from which the new mechanism presented here is verified. This new idea of achieving low-frequency bandgap is of great theoretical significance for controlling low-frequency sound waves.