Incremental learning based fault diagnosis is effective to learn from continuous industrial data on an ongoing basis. However, in the case of non-stationary industrial processes, new data distribution often gradually shifts away from that of historical data, due to equipment aging and manufacturing strategies, etc. Thus, conventional incremental methods with the identical independent distribution (i.i.d) assumption may no longer promise satisfied diagnosis performance. This paper concerns the conditional drift phenomenon, a relaxation of the i.i.d assumption, in which the conditional distribution of industrial data changes within different time. From a mathematical point of view, we firstly give the problem formulation of conditional drift and introduce a target mapping strategy for drift adaptation, under the minimum risk criteria. Then, following this strategy, an incremental diagnosis model with adaptation ability is designed. Particularly, a transformation matrix keeps matching the distributions of historical and new data. Thus, our method can quickly adapt to the conditional drift and be more robust against the evolving environment. The proposed method is applied for diagnosing faults in two industrial processes to demonstrate its effectiveness.