Most traditional false data injection attack (FDIA) detection approaches rely on a key assumption, i.e., the power system can be accurately modeled. However, the transmission line parameters are dynamic and cannot be accurately known during operation and thus the involved modeling errors should not be neglected. In this paper, an illustrative case has revealed that modeling errors in transmission lines significantly weaken the detection effectiveness of conventional FDIA approaches. To tackle this issue, we propose an FDIA detection mechanism from the perspective of transfer learning. Specifically, the simulated power system is treated as a source domain, which provides abundant simulated normal and attack data. The real world's running system whose transmission line parameters are unknown is taken as a target domain where sufficient real normal data are collected for tracking the latest system states online. The designed transfer strategy that aims at making full use of data in hand is divided into two optimization stages. In the first stage, a deep neural network (DNN) is built by simultaneously optimizing several well-designed objective terms with both simulated data and real data, and then it is fine-tuned via real data in the second stage. Several case studies on the IEEE 14-bus and 118-bus systems verify the effectiveness of the proposed mechanism.