import java.text.SimpleDateFormat;
import java.util.Calendar;
import java.util.Date;

public class DateWeekUtil {
    /**
     * 根据日期字符串判断当月第几周
     */
    public static int getWeekOfMonth(String datestr , String format) throws Exception {
        // 将字符串格式化
        SimpleDateFormat sdf = new SimpleDateFormat(format);
        Date date = sdf.parse(datestr);
        Calendar calendar = Calendar.getInstance();
        calendar.setTime(date);
        //第几周
        int week = calendar.get(Calendar.WEEK_OF_MONTH);
        //第几天，从周日开始
        int day = calendar.get(Calendar.DAY_OF_WEEK);
        return week;
    }

    /**
     * 根据日期字符串判断当年第几周
     */
    public static int getWeekOfYear(String datestr , String format) throws Exception {

        // 将字符串格式化
        SimpleDateFormat sdf = new SimpleDateFormat(format);
        Date d = sdf.parse(datestr);
        Calendar calendar = Calendar.getInstance();
        calendar.setTime(d);
        // 第几周
        return calendar.get(Calendar.WEEK_OF_YEAR);
    }


    public static void main(String[] args) throws Exception {
        Date date = new Date();
        String datestr = "2015-05-17" ;
        String format = "yyyy-MM-dd";
        System.out.println("本年第几周："+getWeekOfYear(datestr, format));
        System.out.println("本月第几周："+getWeekOfMonth(datestr, format));

    }

}

测试信息：