By using Lie’s invariance infinitesimal criterion, the continuous equivalence transformations of a class of nonlinear KdV-Burgers equations with variable coefficients are obtained. The differential invariants of order 1 are constructed and the group classification are made starting from the equivalence algebra. At last some general class of variable coefficient nonlinear KdV-Burgers equations are mapped to constant-coefficient Burgers equation, KdV equation and KdV-Burgers equation. In particular, some exact solutions of the variable coefficients KdV-Burgers equation are obtained.