What you can do is remove the _selectedItem initiate in init state and then add a Text() hint for the DropdownButtonWidget as follows. For any help please send me a mail to yashodgayashan@gmail.com.

import 'package:flutter/material.dart';
class DropDownButton extends StatefulWidget {
@override
_DropDownButtonState createState() => _DropDownButtonState();
}
class _DropDownButtonState extends State<DropDownButton> {
  List<ListItem> _dropdownItems = [
    ListItem(1, "First Value"),
    ListItem(2, "Second Item"),
    ListItem(3, "Third Item"),
    ListItem(4, "Fourth Item")
  ];
  List<DropdownMenuItem<ListItem>> _dropdownMenuItems;
  ListItem _selectedItem;
 
  void initState() {
    super.initState();
    _dropdownMenuItems = buildDropDownMenuItems(_dropdownItems);
  }
  List<DropdownMenuItem<ListItem>> buildDropDownMenuItems(List   listItems) {
    List<DropdownMenuItem<ListItem>> items = List();
    for (ListItem listItem in listItems) {
      items.add(
        DropdownMenuItem(
          child: Text(listItem.name),
          value: listItem,
        ),
      );
    }
  return items;
  }
@override
Widget build(BuildContext context) {
  return Scaffold(
    appBar: AppBar(
      title: Text("Flutter tutorial"),
    ),
    body: Column(
      children: <Widget>[
        Row(
        children: <Widget>[
          Container(
            padding: EdgeInsets.all(10.0),
            child: Text(
              "Dropdown",
              style: TextStyle(fontSize: 16.0),
            ),
          ),
          Container(
            padding: EdgeInsets.all(20.0),
            child: DropdownButton<ListItem>(
              hint: Text("Select One"),
              value: _selectedItem,
              items: _dropdownMenuItems,
              onChanged: (value) {
                setState(() {
                _selectedItem = value;
                });
              }
            ),
          ),
        ],
      ),
    ],
  ),
  );
}
}
class ListItem {
  int value;
  String name;
  
  ListItem(this.value, this.name);
}