<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((M^4, g, f)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msup> <mi>M</mi> <mn>4</mn> </msup> <mo>,</mo> <mi>g</mi> <mo>,</mo> <mi>f</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> be a four-dimensional complete noncompact gradient shrinking Ricci soliton with the equation <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Ric+\nabla ^2f= \frac{1}{2}g\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>i</mi> <mi>c</mi> <mo>+</mo> <msup> <mi mathvariant="normal">∇</mi> <mn>2</mn> </msup> <mi>f</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>g</mi> </mrow> </math></EquationSource> </InlineEquation>. If its scalar curvature is 1, Cheng-Zhou [<CitationRef CitationID="CR9">9</CitationRef>] proved that it is a finite quotient of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {R}^2\times \mathbb {S}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> <mo>×</mo> <msup> <mrow> <mi mathvariant="double-struck">S</mi> </mrow> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. In this note we present an alternative proof by analyzing the asymptotic geometry at infinity. In high dimension, we also get similar results under some suitable conditions.</p>