Summary: If \(\mathcal{P}_n\) denotes the class of polynomials of degree at most \(n\), then for \(P\in\mathcal{P}_n\), a consequence of Maximum Modulus theorem yields for \(R>1\), \[\|P(R,.)\|_\infty\le R^n\|P\|_\infty.\] Various generalizations and refinements of this result are available in literature. In this paper, we consider a general class of polynomials \(\mathcal{P}_{n,\mu}\), \(1\le\mu\le n\), with restriction on zeros in a specific way and obtain Zygmund-type inequalities concerning the growth of polynomials. Besides obtaining a refinement of a result due to A. Aziz and the second author [Math. Inequal. Appl. 7, No. 3, 379–391 (2004; Zbl 1061.30001)], we improve a result of A. Aziz and N. A. Rather [Proc. Indian Acad. Sci., Math. Sci. 109, No. 1, 65–74 (1999; Zbl 0934.30002)].