procedure MoveTreeNode (const aTreeView : TTreeView;
                        const aNode : TTreeNode;
                        const aDirection : Integer);
var
  Sibling : TTreeNode;
begin
  if (aNode = nil) then
    Exit;

  if (aDirection < 0)
    then Sibling := aNode.getPrevSibling
    else Sibling := aNode.getNextSibling;

  if (Sibling = nil) then
    Exit;

  aTreeView.Items.BeginUpdate;
  try
    if (aDirection < 0) then
      aNode.MoveTo (Sibling, naInsert)
    else
      Sibling.MoveTo (aNode, naInsert);
  finally
    aTreeView.Items.EndUpdate;
  end;
end;

// Anwendung

MoveTreeNode (TreeView1, TreeView1.Selected, -1); // Knoten nach oben schieben
MoveTreeNode (TreeView1, TreeView1.Selected, +1); // Knoten nach unten schieben