  We calculate the Adler $D$-function for ${\cal N}=1$ SQCD in the three-loop
approximation using the higher covariant derivative regularization and the
NSVZ-like subtraction scheme. The recently formulated all-order relation
between the Adler function and the anomalous dimension of the matter
superfields defined in terms of the bare coupling constant is first considered
and generalized to the case of an arbitrary representation for the chiral
matter superfields. The correctness of this all-order relation is explicitly
verified at the three-loop level. The special renormalization scheme in which
this all-order relation remains valid for the $D$-function and the anomalous
dimension defined in terms of the renormalized coupling constant is constructed
in the case of using the higher derivative regularization. The analytic
expression for the Adler function for ${\cal N}=1$ SQCD is found in this scheme
to the order $O(\alpha_s^2)$. The problem of scheme-dependence of the
$D$-function and the NSVZ-like equation is briefly discussed.
