An exhaust gas purifying catalyst comprising: a crystalline metal oxide support and noble metal particles supported on said support, wherein said noble metal particles are epitaxially grown on said support, wherein said noble metal particles are dispersed and supported on the outer and inner surfaces of said support, wherein said noble metal particles are supported in a generally hemispherical shape on said support, wherein the width of the portion of contact between said support and at least one noble metal particle and the height of said at least one noble metal particle from the surface of said support satisfy the following formula: W / H > 1.0 wherein the height of said at least one noble metal particle from the surface of said support is 0.5 nm or more, and wherein the particle diameter of said noble metal particles as measured by a carbon monoxide adsorption method is from 0.5 to 10 nm, wherein said noble metal is platinum, wherein said support is ceria or a ceria-zirconia solid solution, and wherein the exhaust gas purifying catalyst is produced by masking, in a solution, at least a part of the surface of a crystalline metal oxide support by a masking agent, introducing said support with at least a part of the surface being masked by a masking agent, into a noble metal-containing solution containing a noble metal, and drying and firing said support and said noble metal-containing solution to support said noble metal on said support, wherein said masking agent is terephthalic acid, isophthalic acid, trimesic acid or pyromellitic acid, wherein said noble metal-containing solution is a noble metal aggregate-containing solution containing a partially reduced and aggregated noble metal aggregate, wherein said noble metal aggregate-containing solution is obtained by providing a raw material solution containing a noble metal ion and/or complex and a polymer, coordinating said noble metal ion and/or complex to said polymer, and partially reducing and aggregating said noble metal ion and/or complex coordinated to said polymer, and wherein said partial reduction and aggregation are performed by heating, addition of a reducing agent, or a combination thereof. a crystalline metal oxide support and noble metal particles supported on said support, wherein said noble metal particles are epitaxially grown on said support, wherein said noble metal particles are dispersed and supported on the outer and inner surfaces of said support, wherein said noble metal particles are supported in a generally hemispherical shape on said support, wherein the width of the portion of contact between said support and at least one noble metal particle and the height of said at least one noble metal particle from the surface of said support satisfy the following formula: W / H > 1.0 wherein the height of said at least one noble metal particle from the surface of said support is 0.5 nm or more, and wherein the particle diameter of said noble metal particles as measured by a carbon monoxide adsorption method is from 0.5 to 10 nm, wherein said noble metal is platinum, wherein said support is ceria or a ceria-zirconia solid solution, and wherein the exhaust gas purifying catalyst is produced by masking, in a solution, at least a part of the surface of a crystalline metal oxide support by a masking agent, introducing said support with at least a part of the surface being masked by a masking agent, into a noble metal-containing solution containing a noble metal, and drying and firing said support and said noble metal-containing solution to support said noble metal on said support, wherein said masking agent is terephthalic acid, isophthalic acid, trimesic acid or pyromellitic acid, wherein said noble metal-containing solution is a noble metal aggregate-containing solution containing a partially reduced and aggregated noble metal aggregate, wherein said noble metal aggregate-containing solution is obtained by providing a raw material solution containing a noble metal ion and/or complex and a polymer, coordinating said noble metal ion and/or complex to said polymer, and partially reducing and aggregating said noble metal ion and/or complex coordinated to said polymer, and wherein said partial reduction and aggregation are performed by heating, addition of a reducing agent, or a combination thereof.