The dispersion curve of a one-dimensional linear diatomic periodic chain comprises two distinct branches: acoustic and optical, separated by a Bragg band gap whose width is influenced by the ratio of atomic masses. Introducing a cubic nonlinear spring to the masses within this chain creates a novel nonlinear periodic structure, enabling the modulation of the band gap without altering the atomic mass ratio. This paper derives the linear dispersion relationship for the diatomic periodic chain, revealing how the base spring introduces a fresh band gap within the quasi-static (QS) frequency range, with the band gap’s characteristics varying according to different linear parameters. In the numerical analysis section, we establish mathematical models for both semi-infinite and finite-length periodic chains. The semi-infinite models are simulated by incorporating a perfectly matched layer (PML) at the chain’s terminus. The findings indicate that, when the excitation frequency approximates the boundary of the Bragg band gap, a pronounced standing wave effect emerges in the periodic chain, exacerbated by the mass disparity. At the boundary frequency, the significant amplitude of the mass block within the unit cell amplifies the influence of nonlinear factors, thereby enabling the regulation of the structural band gap through the application of minimal excitation amplitudes. Furthermore, the expansion or contraction of the Bragg band gap can be achieved by applying springs with either soft or hard nonlinear characteristics to atoms of differing masses.