Conventional interference alignment (IA) for a MIMO interference channel (IFC) requires global and perfect channel state information at transmitter (CSIT) to achieve the optimal degrees of freedom (DoF), which prohibits practical implementation. In order to alleviate the global CSIT requirement caused by the coupled relation among all of IA equations, we propose an IA scheme with a single feedback link of each receiver in a limited feedback environment for a three-user MIMO IFC. The main feature of the proposed scheme is that one of users takes out a fraction of its maximum number of data streams to decouple IA equations for three-user MIMO IFC, which results in a single link feedback structure at each receiver. While for the conventional IA each receiver has to feed back to all transmitters for transmitting the maximum number of data streams. With the assumption of a random codebook, we analyze the upper bound of the average throughput loss caused by quantized channel knowledge as a function of feedback bits. Analytic results show that the proposed scheme outperforms the conventional IA scheme in term of the feedback overhead and the sum rate as well.