<p>In this paper, we are concerned with the 2D damped wave-type magnetohydrodynamic system (abbreviated as MHD-wave system). The purpose of this paper is to study the large-time behavior of solutions to the MHD-wave system, especially to investigate the influence of the bad term <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma \partial _{tt}b\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <msub> <mi>∂</mi> <mrow> <mi mathvariant="italic">tt</mi> </mrow> </msub> <mi>b</mi> </mrow> </math></EquationSource> </InlineEquation> on the large-time behavior. Rates of decay are obtained for both the solutions and higher derivatives in different Sobolev spaces with explicit rates of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>. This decay behavior matches the rates established for the standard MHD system in the works of Agapito and Schonbek (Partial Differ Equ 32:1791–1812, 2007) and Schonbek et al. (Partial Differ Equ Math Ann 304:717–756, 1996) under the same norm, particularly in the limit regime where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\gamma \rightarrow 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>