<p>In this paper, we give the analysis of Kelvin-Helmholtz instability in three-dimensional magnetohydrodynamics(MHD) flows which gives a rigorous confirmation that transverse magnetic field does have a destabilizing effect on the Kelvin-Helmholtz instability. The transverse magnetic field plays its role in ideal MHD comes through pressure contributions modifying the characteristic magneto-sonic wave speed. When the magnitude of the magneto-acoustic Mach number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(M_{B}:=\frac{\dot{v}_{1}^{+}}{C_{B}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>M</mi> <mi>B</mi> </msub> <mo>:</mo> <mo>=</mo> <mfrac> <msubsup> <mover accent="true"> <mi>v</mi> <mo>˙</mo> </mover> <mrow> <mn>1</mn> </mrow> <mo>+</mo> </msubsup> <msub> <mi>C</mi> <mi>B</mi> </msub> </mfrac> </mrow> </math></EquationSource> </InlineEquation> is strictly between some fixed small enough constant <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\epsilon _{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϵ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sqrt{2}-\epsilon _{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msqrt> <mn>2</mn> </msqrt> <mo>-</mo> <msub> <mi>ϵ</mi> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>, we can prove the linear and nonlinear ill-posedness of the Kelvin-Helmholtz problem for compressible MHD flows.</p>