from tkinter import *

root = Tk()

mylist = ['one', 'two', 'three']

var = StringVar(value=mylist)
box = Listbox(master=root, listvariable=var)
box.pack(fill=BOTH, expand=True)

mylist.append('four')
mylist.remove('two')
mylist.insert(3, mylist.pop(1))

var.set(mylist)

root.mainloop()