Because blind adaptive beamforming algorithms do not depend on any reference signal, they have found numerous important applications in signal processing. However, the conventional constrained constant modulus algorithm (CMA) may suffer significant performance degradation in the presence of the slight mismatches between the actual and assumed signal steering vectors. In this paper, to combat the mismatches, a novel robust constrained CMA is proposed for implementing double constraints with recursive method updating, which is based on explicit modeling of uncertainties in the desired signal array response. The proposed robust constrained CMA provides an improved robustness against the signal steering vector mismatches, enhances the array system performance under random perturbations in sensor parameters and makes the mean output array SINR consistently close to the optimal one. The performance of the proposed algorithm is compared with that of linear constrained CMA algorithm by computer simulations, the results of which demonstrate a marked improvement in the robustness against signal steering vector mismatches.