There are a couple of code issues.
1) You must use add calendar.add(Calendar.MONTH, -1);to subtract the month.
2) , month_name : Dec-2016, SimpleDateFormat , .. Y, Week year Y .
SimpleDateFormat .
:
public static void main (String[] args) throws java.lang.Exception
{
SimpleDateFormat month_date = new SimpleDateFormat("MMM-yyyy");
Calendar calendar = Calendar.getInstance();
calendar.add(Calendar.MONTH, -1);
String month_name = month_date.format(calendar.getTime());
System.out.println("month_name : "+month_name);
}