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The long-term sensor drift phenomenon seriously restricts the performance of Electronic Nose (E-nose) systems in their various applications. Due to frequent recalibrations, traditional drift compensation methods are costly and laborious, and their performance are limited due to the nonlinear dynamic properties of the drift. The latest proposed Broad Learning System (BLS) has been confirmed to be an efficient and effective learning technique for many machine learning problems. However, BLS with cross-domain learning capability has rarely been studied. In this paper, a novel unified framework called Domain Transfer Broad Learning System (DTBLS) is proposed based on BLS, to address the issue of drift via adaptive compensation. For the case where there is no labeled target sample, with simultaneous considerations of the empirical loss of source data, marginal distribution adaptation, conditional distribution adaptation and manifold regularization, the DTBLS framework learns a robust target classifier by using labeled source data and unlabeled target data to compensate the drift of sensor response adaptively. To the best of our knowledge, DTBLS is the first BLS-based transfer learning framework for the problem of dataset shift existing in E-nose systems. Like the basic BLS, high computation efficiency is achieved due to the existence of analytical solution. Parameter sensitivity analysis is also conducted to show that the optimal solution can be obtained in a wide range. Experiments on a public gas sensor drift dataset demonstrate that the proposed method outperforms the state-of-the-art methods well.