This work proposes constrained constant modulus unscented Kalman filter (CCM-UKF) algorithm and its low-complexity version called reduced-rank constrained constant modulus unscented Kalman filter (RR-CCM-UKF) algorithm for blind adaptive beamforming. In the generalized sidelobe canceller (GSC) structure, the proposed algorithms are devised according to the CCM criterion. Firstly, the cost function of the constrained optimization problem is transformed to suit the Kalman filter-style state space model. Then, the optimum weight vector of the beamformer can be estimated by using the recursive formulas of UKF. In addition, the a priori parameters of UKF (system and measurement noises) are processed adaptively in the implementation. Simulation results demonstrate that the proposed algorithms outperform the existing methods in terms of convergence speeds, output signal-to-interference-plus-noise ratios (SINRs), mean-square deviations (MSDs) and robustness against steering mismatch.