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A variable step-size (VS) algorithm is proposed based on the pre-filter bank (pfb) adaptive algorithm, first introduced by Courville and Duhamel (1998). The proposed algorithm adjusts the step-sizes of the subbands by using a simplified version of the Benveniste procedure (Ang et al. (2001)). As the filter banks are commonly narrowband filters, their nondecimated outputs are highly correlated. This correlation allows us to approximate the subband autocorrelation matrices by single rank matrices, thus permitting us to simplify and reduce the computational complexity of the VS procedures. The proposed inexpensive algorithm is very efficient in terms of tracking capabilities and initial learning for environments with colored additive noise and colored input signal.