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This paper proposes a new transform-domain approximate QR least-squares-based (TA-QR-LS) algorithm for adaptive Volterra filtering (AVF). It improves the approximate QR least-squares (A-QR-LS) algorithm for multichannel adaptive filtering by introducing a unitary transformation to decorrelate the input signal vector so as to achieve better convergence and tracking performances. Further, the Givens rotation is used instead of the Householder transformation to reduce the arithmetic complexity. Simulation results show that the proposed algorithm has much better initial convergence and steady state performance than the LMS-based algorithm. The fast RLS AVF algorithm [J. Lee and V. J. Mathews, Mar 1993] was found to exhibit superior steady state performance when the forgetting factor is chosen to be 0.995, but the tracking performance of the TA-QR-LS algorithm was found to be considerably better.