  For a plane curve, a point on the projective plane is said to be Galois if
the projection from the point as a map from the curve to a line induces a
Galois extension of function fields. We present upper bounds for the number of
Galois points, if the genus is greater than zero. If the curve is not an
immersed curve, then we have at most two Galois points. If the degree is not
divisible by two nor three, then the number of outer Galois points is at most
three. As a consequence, a conjecture of Yoshihara is true in these cases.
