doctor faustus is a mority play?

No, Dr. Faustus is not a typical morality play. Morality plays are intended to teach a lesson, the difference between good and evil or sin and virtue, for example. Morality plays are also representative, characters are allegorical and don't undergo major changes. Faustus does not fit with this description.

Regardless, there are aspects to Dr Faustus that do parallel the morality play. For example, we have the theme of sin and redemption (the characters are not allegorically represented, but the theme is there). The play deals with the Devil, temptation, and the seven deadly sins.