By default, the menu of a combobox only shows eight items. If there are more items in the menu, a scrollbar is automatically created. To change the default of eight, use JComboBox.setMaximumRowCount(). 
    // Create a read-only combobox with lots of items
    String[] items = new String[50];
    for (int i=0; i<items.length; i++) {
        items[i] = "" + Math.random();
    }
    JComboBox cb = new JComboBox(items);
    
    // Retrieve the current max visible rows
    int maxVisibleRows = cb.getMaximumRowCount();
    
    // Change the current max visible rows
    maxVisibleRows = 20;
    cb.setMaximumRowCount(maxVisibleRows);