In　this　paper　we　investigate　the　existence　and　time-decay　rates　of　strong　solutions　with　small　perturbation　to　the　systems　of　equations　of　a　compressible　magnetohydrodynamic　fluid　with　nonlinear　damping.　First　we　reformulate　the　system　into　a　perturbation　form.　Then　we　establish　a　priori　estimates　of　solutions,　and　prove　the　existence　of　the　global-in-time　based　on　the　local　existence　of　unique　solutions.　Finally　we　will　establish　the　optimal　time-decay　rates　of　the　non-homogeneous　system　by　constructing　some　decay　estimates　of　the　linearized　system　based　on　the　decomposition　technique　of　both　the　low　and　high　frequencies　of　solutions　as　in　[40].　©　2022　Elsevier　Inc.