How can I show dropdown list in text field using JavaScript?

I have a text field where user can insert some value. I want to make some dropdown list in this text field, where user can see and choose values from array. For example, when focus is on this field, user can click some button (arrow down) to see this dropdown list and to choose one of the values. Or user can insert new value. The important thing is that it's not an autocomplete - user should always see all values of the array, regardless of what he inserted into textfield.

How can I make the part about showing dropdown list in textfield using JavaScript?