Reservoir classification is an essential step for the exploration and production process in the oil and gas industry. An appropriate automatic reservoir classification will not only reduce the manual workloads of experts, but also help petroleum companies to make optimal decisions efficiently, which in turn will dramatically reduce the costs. Existing methods mainly focused on generating reservoir classification in a single geological block but failed to work well on a new oilfield block. Indeed, how to transfer the subsurface characteristics and make accurate reservoir classification across the geological oilfields is a very important but challenging problem. To that end, in this paper, we present a focused study on the cross-oilfield reservoir classification task. Specifically, we first propose a Multi-scale Sensor Extraction (MSE) to extract the multi-scale feature representations of geological characteristics from multivariate well logs. Furthermore, we design an encoder-decoder module, Specific Feature Learning (SFL), to take advantage of specific information of both oilfields. Then, we develop a Knowledge-Attentive Transfer (KAT) module to learn the feature-invariant representation and transfer the geological knowledge from a source oilfield to a target oilfield. Finally, we evaluate our approaches by conducting extensive experiments with real-world industrial datasets. The experimental results clearly demonstrate the effectiveness of our proposed approaches to transfer the geological knowledge and generate the cross-oilfield reservoir classifications.