Batch processes in the biopharmaceutical and chemical manufacturing industries often develop new products to meet changing market demands. When the dynamic models of these new products are trained, dynamic modeling with limited data for each product can lead to inaccurate results. One solution is to extract useful knowledge from past historical production data that can be applied to the product of a new grade. In this way, the model can be built quickly without having to wait for additional modeling data. In this study, a subspace identification combined common feature learning scheme is proposed to quickly learn a model of a new grade. The proposed modified state-space model contains common and special parameter matrices. Past batch data can be used to train common parameter matrices. Then, the parameters can be directly transferred into a new SID model for a new grade of the product. The new SID model can be quickly well trained even though there is a limited batch of data. The effectiveness of the proposed algorithm is demonstrated in a numerical example and a case of an industrial penicillin process. In these cases, the proposed common feature extraction for the SID learning framework can achieve higher performance in the multi-input and multi-output batch process regression problem.