<p>In this paper, using the space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2024_2343_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="250" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{2}([a,b]\times [c,d])\times C[0,T],(T&lt;1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mrow> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> </mrow> <mo>×</mo> <mrow> <mo stretchy="false">[</mo> <mi>c</mi> <mo>,</mo> <mi>d</mi> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">)</mo> </mrow> <mo>×</mo> <mi>C</mi> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mi>T</mi> <mo stretchy="false">]</mo> </mrow> <mo>,</mo> <mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo>&lt;</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, we have introduced a new and efficient approach to a discontinuous kernel solution of (2 + 1) dimensional mixed Volterra–Fredholm integral equations (<b>MVFIE</b>). By applying the separation of variables approach, the (<b>2 + 1</b>) dimensional <b>MVFIE</b> has been reduced to a two-dimensional Fredholm integral Eq.&#xa0;(<b>2D-FIE</b>). Next, we derive a system of linear algebraic equations using the Chebyshev polynomials of the sixth-kind (<b>CP6K</b>) approach. We are demonstrating that the integral equations solution exists and unique. Convergence of solutions has been proven. Numerical simulations have been given to verify that the new method produces more efficient and better results. The error in each example is computed by using Maple software.</p>