A projective variety in a projective space is said to be p -linear if it is p -regular and has no defining equation of degree < p. It is well known that 2 -linear varieties are exactly varieties of minimal degree. In this paper, we study 3 -linear varieties of codimension 2. We classify all smooth 3 -linear varieties of codimension 2. There are six kinds of such varieties. Also, we provide some nonconic singular 3 -linear varieties of codimension 2.