Let C be a projective plane curve of degree d whose singularities are all isolated. Suppose C is not concurrent lines. Ploski proved that the Milnor number of an isolated singlar point of C is less than or equal to (d-1)(2) - [d/2]. In this paper, we prove that the Milnor sum of C is also less than or equal to (d-1)(2) - [d/2] and the equality holds if and only if C is a Ploski curve. Furthermore, we find a bound for the Milnor sum of projective plane curves in terms of GIT.