You can set the property ListViewItem.BackColor, however, this must be done manually for each alternating line. Alternatively, you can use DataGridViewone that has a property AlternateRowStylethat will do this automatically - although you need to bind data to your rows in a collection, which is a whole different topic.
For a simple case:
foreach (ListViewItem item in listView1.Items)
{
item.BackColor = item.Index % 2 == 0 ? Color.Red : Color.Black;
}