The complex fast fixed-point algorithm, also called complex FastICA, is one of the most important algorithms for Blind Signal Separation (BSS). However, the performance of this algorithm deteriorates when it is used to separate the noisy mixed sources, especially in the low SNR case, since the covariance matrix of whitened observations is not an identity matrix but a diagonal matrix. This paper bases on the present complex FastICA. First, the mixed sources defined with complex Independent Component Analysis (ICA) signal model are projected onto the signal subspace. Thus, the denoising and decorrelating from mixed signal samples can be handily achieved. Then, the learning rule of the algorithm is modified, where the effect of white Gaussian noise is taken into account. Therefore，the BSS performance of complex FastICA is improved markedly. In this paper, the learning rule of denoised noncircular FastICA (nc-FastICA) is derivated and the detailed procedure is given. Simulation results demonstrate the effectiveness of the proposed algorithm.