See article here:
ComboBox with Suggest Ability based on Substring-Search[
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As you may find using a Binding source is overkill, you can also try this:
this.comboBox1.DropDownStyle = ComboBoxStyle.DropDown;
this.comboBox1.AutoCompleteMode = AutoCompleteMode.SuggestAppend;
this.comboBox1.AutoCompleteSource = AutoCompleteSource.ListItems;
this.comboBox1.Items.Add("One");
this.comboBox1.Items.Add("Two");
this.comboBox1.Items.Add("Three");
this.comboBox1.Items.Add("Four");