Автор: http://www.swissdelphicenter.ch

procedure Shuffle(var aArray; aItemCount: Integer; aItemSize: Integer);
{ after Julian M Bucknall }
var
  Inx: Integer;
  RandInx: Integer;
  SwapItem: PByteArray;
  A: TByteArray absolute aArray;
begin
  if (aItemCount > 1) then
  begin
    GetMem(SwapItem, aItemSize);
    try
      for Inx := 0 to (aItemCount - 2) do
      begin
        RandInx := Random(aItemCount - Inx);
        Move(A[Inx * aItemSize], SwapItem^, aItemSize);
        Move(A[RandInx * aItemSize], A[Inx * aItemSize], aItemSize);
        Move(SwapItem^, A[RandInx * aItemSize], aItemSize);
      end;
    finally
      FreeMem(SwapItem, aItemSize);
    end;
  end;
end;

procedure TForm1.Button1Click(Sender: TObject);
var
  a: array[1..10] of Integer;
  i: Shortint;
begin
  Randomize;
  for i := Low(a) to High(a) do
    a[i] := i;
  Shuffle(a, High(a), SizeOf(Integer));
  for i := 1 to High(a) - 1 do
    ListBox1.Items.Add(IntToStr(a[i]));
end;