Let \(X\) be a smooth projective surface and \(D\) be an effective \(\mathbb{Q}\)-divisor on \(X\). Zariski proved the following fundamental theorem in surface theory: The divisor \(D\) can be uniquely written as \(D=P+N\), such that \(P\) is nef, \(N\) is zero or has negative definite intersection matrix and \(P\cdot C=0\) for every irreducible component \(C\) of \(N\). In this note, the author gives a simple proof of this Zariski decomposition. The method may be used to a practical algorithm for computation of \(P\). The idea of this simple proof is that the positive part \(P\) can be constructed as a maximal nef subdivisor of \(D\).