MOTIVATION: Position weight matrices (PWMs) are widely used to depict the DNA binding preferences of transcription factors (TFs) in computational molecular biology and regulatory genomics. Thus, learning an accurate PWM to characterize the binding sites of a specific TF is a fundamental problem that plays an important role in modeling regulatory motifs and also in discovering the regulatory targets of TFs. RESULTS: We study the question of how to learn a more accurate PWM from both binding sequences and gene expression (or ChIP-chip) data, and propose to find a PWM such that the likelihood of simultaneously observing both binding sequences and their associated gene expression (or ChIP-chip) data is maximised. To solve the above maximum likelihood problem, a sequence weighting scheme is thus introduced based on the observation that binding sites inducing drastic fold changes in mRNA expression (or showing strong binding ratios in ChIP experiments) are likely to represent a true motif. We have incorporated this new learning approach into the popular motif finding program AlignACE. The modified program, called W-AlignACE, is compared with three other programs (AlignACE, MDscan and MotifRegressor) on a variety of datasets, including simulated data, mRNA expression and ChIP-chip data. These tests demonstrate that W-AlignACE is an effective tool for discovering TF binding motifs from gene expression (or ChIP-chip) data and, in particular, has the ability to find very weak motifs like DIG1 and GAL4. AVAILABILITY: http://www.ntu.edu.sg/home/ChenXin/Gibbs