We propose a novel approach to proving the termination of imperative programs by k-induction. By our approach, the termination proving problem can be formalized as a k-inductive invariant synthesis task. On the one hand, k-induction uses weaker invariants than that required by the standard inductive approach. On the other hand, the base case of k-induction, which unrolls the program, can provide stronger pre-condition for invariant synthesis. As a result, the termination arguments of our approach can be synthesized more efficiently than the standard method. We implement a prototype of our k-inductive approach. The experimental results show the significant effectiveness and efficiency of our approach.