you can check and add items if not already added using
listBox.Items.FindByValue
but you have to loop though each and every item. easy way is fist clear items and add items again.
protected void Timer1_Tick1(object sender, EventArgs e)
{
LstBox.Items.Clear();
string[] str;
ftp = new FTPOperations();
str = ftp.GetFileList("DCU/INST_VAL");
foreach (string value in str)
{
LstBox.Items.Add(value);
}
Label1.Text = DateTime.Now.ToShortTimeString();
}