I got married last June 20th 2013 and my wife was tested pregnant on July 20th 2013 her last mensurational period was 05 may 2013, and now her delivery date is march 17th 2014 is this correct delivery period

Predicting date of conception is just a guess using 2 weeks after the last menstrual period as the norm, and length of a pregnancy varies, so due date is never exact. She didn't have had a period between May 5 and June 20, when most women would have, so if you didn't have sex before marriage and get pregnant immediately, the due date is probably going to be based now on ultrasound pictures. But it can still be about 2 weeks before, or 2 weeks after, what the doctor predicts!

Assuming she got pregnant right after marriage, yes it is about right.

Most dates are estimates and will be refined as the delivery time gets closer.