In this paper, we shall prove some integral mean estimates for polynomials having zeros inside a circle. Our results generalize and refine some known polynomial inequalities. If  is a polynomial of degree n having all its zeros in    for      and  with  it is known that

We shall present a generalization and refinement of this result by involving the location of all the zeros of the polynomial  Besides this, we shall also consider the case when and extend many known results.

polynomial, maximum modulus, integral mean estimates.