In this paper, new upper bounds for the solution matrix of the continuous algebraic Riccati matrix equation (CARE) are derived by means of some matrix inequalities and linear algebraic techniques. Furthermore, for the derived each bound, iterative algorithms are developed to obtain sharper solution estimates. Comparing with some appearing results in the literature, the presented bounds are less restrictive and more efficient. Finally, numerical examples are given to illustrate the effectiveness of the proposed results. © 2013 The Franklin Institute.