The authors improve the boundedness theorems of the Marcinkiewicz integral \(\mu_\Omega\) on \(\roman{BMO}(\mathbb R^n)\) and the Campanato spaces \(\mathcal E^{\alpha, p}(\mathbb R^n)\). Recall the Campanato spaces. A locally integrable function \(f(x)\) is said to belong to \(\mathcal E^{\alpha, p}(\mathbb R^n)\) if \(\|f\|_{\alpha,p}=\sup_Q |Q|^{-\alpha/n}\bigl(|Q|^{-1}\int_Q|f(x)-f_Q|^p dx \bigr)^{1/p}\alpha\geq -n/p)\). We also recall the Marcinkiewicz integral with homogeneous symbols, defined first by E.~M.~Stein. Let \(\Omega\in L^1(S^{n-1}) \) be homogeneous of degree zero and have the cancellation property \(\int_{S^{n-1}}\Omega(x') d\sigma(x')=0\). Then the Marcinkiewicz integral of higher dimension is defined by \(\mu_\Omega (f)(x)=\bigl(\int_{0}^{\infty}|F_{\Omega, t}(x)|^2t^{-3} dt\bigr) ^{1/2}\), where \(F_{\Omega, t}(x)=\int_{|x-y|\leq t}\Omega(x-y)|x-y|^{1-n}f(y) dy\). To state the authors' results, recall the \(L^q\) modulus of continuity, \(\omega_q(\delta)\), defined by \(\omega_q(\delta) =\sup_{\|\rho-I\|\leq \delta}\bigl(\int_{S^{n-1}}|\Omega(\rho x')-\Omega(x')|^q d\sigma(x') \bigr)^{1/q}\), where \(\rho\) is a rotation on \(S_{n-1}\) and \(I\) is the identity operator. The authors' results are as follows: Let \(\Omega \in L^q(S^{n-1})\) satisfy the cancellation property and \(\int_{0}^{1}\omega_q(\delta)\delta^{-1}(1+|\log \delta|)^\varepsilon d\delta 2\). Then, for \(f\in \roman{BMO}(\mathbb R^n)\) satisfying \(\mu_\Omega(f)(x)0\) in the case \(0<\alpha<1\), and by \(\int_{0}^{1}\omega_q(\delta)\delta^{-1} d\delta<\infty\) in the case \(\alpha<0\). These results improve the known ones by \textit{Y. Han} [Acta Sci. Nat. Univ. Pekinensis 5, 799-839 (1987)]and by \textit{S. Qiu} [J. Math. Res. Exp. 12, No. 1, 41-50 (1992; Zbl 0773.42014)].