[*Caro*]

Hola, puedes utilizar FindFirst y FindNext.

Código Delphi [-]
var
 Path : String;
 sr: TSearchRec;
begin
 if SelectDirectory('Seleccione la ruta del directorio', '', Path) then
  begin
   Try
     Path := IncludeTrailingPathDelimiter(Path);
 
     if FindFirst(Path + '*.zip', faArchive, sr) = 0 Then
      repeat
        Memo1.Lines.Add(sr.Name);
      until FindNext(sr) <> 0;
   Finally
    FindClose(sr);
  end;

Saluditos