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In this paper, we propose a novel adaptive filtering algorithm named adaptive parallel variable-metric projection (APVP) algorithm, which includes the proportionate normalized least mean square (PNLMS) algorithm as its special example. The proposed algorithm is based on parallel projection (onto multiple closed convex sets) with time-varying metrics. A convergence analysis of the proposed algorithm is presented with the aid of the adaptive projected subgradient method. Numerical examples demonstrate that the proposed algorithm realizes echo cancellation superior to the conventional algorithms.