The binding energy of the impurity in an asymmetric quantum well subjected to a longitudinal electric field is calculated using a variational method. The dependence of the impurity binding energy on the asymmetry of the well, the external electric field, the impurity position and the well width is investigated. It is shown that the asymmetry of the well affects the impurity state effectively. For two kinds of asymmetric structures used in our calculation, the difference of the impurity binding energy varies with increasing field. This difference stays a positive value for the impurity located at z(i) > 0 within a narrower as well as in a wider well. When the impurity is at z(i) < 0, the difference for a wider well reverses sign, being negative for low field and positive for high field, while it stays negative for a narrower well with increasing field.