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In this paper, a novel conjugate-gradient based complex independent component analysis algorithm (CBC- ICA) for processing complex signals is presented, which employs independent conjugate-gradient based search directions, rather than the gradient directions, for the real and imaginary components of the weight vector. The proposed technique is used to perform interference suppression for diversity QPSK receivers in time-varying channels. In contrast to the well known Complex FastICA algorithm, the CBC-ICA demonstrates fast convergence in dynamic environments, while maintaining satisfactory symbol error rate (SER) performance. In addition, the performance of the CBC-ICA is preserved for large processing block sizes.