In this paper, we present a new Capon-like blind receiver based on linearly constrained constant modulus (LCCM) criterion for the multiple-input multiple-output (MIMO) antennas system along with space–time block code (ST-BC) using direct-sequence code division multiple access (CDMA) modulation technique. A time-varying channel model with generalized sidelobe canceller (GSC) associated with the recursive least squares (RLS) algorithm is implemented to reduce the complexity of receiver design. In our derived algorithm, the parameter of constant modulus, α, relating to the desired user power is updated adaptively via stochastic gradient algorithm to track user’s amplitude variation. Also we prove theoretically that in the two-branch filter bank receiver design the weight vector of one branch can be updated simply using the other one, which has been obtained with our proposed CM-GSC-RLS algorithm, with simple pre-calculated transform. Hence computation complexity of the proposed adaptive blind receiver can be further reduced significantly. Via intense simulations it reveals that our proposed scheme has robust performance against the user’s acquisition inaccuracies comparing with current available algorithms.