This paper presents a method of constructing algebraic geometry codes with many automorphisms arising from Galois points for algebraic curves. This enables us to construct codes with automorphisms systematically, and gives a geometric interpretation of a condition in a well-known criterion by Stichtenoth for yielding automorphisms of AG codes. Compared with Stichtenoth’s criterion, the main theorem does not require a condition on the genus. The proof relies on techniques from algebraic geometry, more precisely on investigating actions of automorphisms on a linear system coming from a morphism to a projective plane. This paper also provides a generalization of the main theorem, which recovers several known one-point AG codes with automorphisms.