  We generalize the celebrated heavy quark expansion to nonlocal QCD operators.
By taking nonlocal heavy-light current on the light-cone as an example, we
confirm that the collinear singularities are common between QCD operator and
the corresponding operator in heavy quark effective theory (HQET), at the
leading power of $1/M$ expansion. Based on a perturbative calculation in
operator form at one-loop level, a factorization formula linking QCD and HQET
operators is investigated and the matching coefficient is determined. The
matching between QCD and HQET light-cone distribution amplitudes (LCDAs) as
well as other momentum distributions of hadron can be derived as a consequence.
