We define the equivariant Chern-Schwartz-MacPherson class of a possibly singular algebraic G-variety over the base field C, or more generally over a field of characteristic 0. In fact, we construct a natural transformation C ∗ from the G-equivariant constructible function functor F to the G-equivariant homology functor H ∗ or A ∗ (in the sense of Totaro-EdidinGraham). This C ∗ may be regarded as MacPherson’s transformation for (certain) quotient stacks. We discuss on other type Chern classes and applications. The Verdier-Riemann-Roch formula takes a key role throughout.