In this paper, we propose a novel low-complexity variable forgetting factor (VFF) mechanism to enhance the performance of recursive least squares (RLS) algorithms for adaptive blind beamforming. The beamformer is designed according to the constrained constant modulus (CCM) criterion, and the proposed algorithm operates in the generalized sidelobe canceler (GSC) structure for implementation. The proposed variable forgetting factor mechanism employs a new component updated by the time average of the constant modulus (CM) cost function, to adjust the forgetting factor. A complexity comparison is provided to show its advantages over existing methods. The study of the steady-state analysis is carried out. Simulation results which are presented for a nonstationary scenario illustrate that the proposed variable forgetting factor mechanism achieves a superior performance compared to existing algorithms.1