Next quarter without using Quarter function
mysql&gt; SELECT CONCAT_WS('-', YEAR(NOW()), MONTH(NOW()), '01') + INTERVAL
       3 * QUARTER(NOW()) + 1 - MONTH(NOW())
       MONTH;
--&gt; 2016-07-01 


If you don't need the date of the beginning of the next quarter, but need the string '3rd quarter July-September', then use a CASE clause.

Without QUARTER:

SELECT CONCAT_WS('-', YEAR(NOW()), MONTH(NOW()), '01') + INTERVAL
       3 * FLOOR(MONTH(NOW())/3+1) + 1 - MONTH(NOW())
       MONTH;


Because QUARTER(x) is the same as FLOOR(MONTH(x)/3+1).