Software Transactional Memory systems (STMs) have garnered significant interest as an elegant alternative for addressing synchronization and concurrency issues with multi-threaded programming in multi-core systems. In order for STMs to be efficient, they must guarantee some progress properties. This work explores the notion of starvation-freedom in Software Transactional Memory Systems (STMs). A STM systems is said to be starvation-free if every thread invoking a transaction gets opportunity to take a step (due to the presence of a fair scheduler) then the transaction will eventually commit. A few starvation-free algorithms have been proposed in the literature in the context of single-version STM Systems. These algorithm work on the basis of priority. If two transactions conflict, then the transaction with lower priority will abort. A transaction running for a long time will eventually have the highest priority and hence commit. But the drawback with this approach is that if a set of high-priority transactions become slow then they can cause several other transactions to abort. In that case, this approach becomes similar to pessimistic lock-based approach. Multi-version STMs maintain multiple-versions for each transactional object or t-object. By storing multiple versions, these systems can achieve greater concurrency. In this paper, we propose a multi-version starvation free STM, KSFTM, which as the name suggests achieves starvation freedom while storing K versions of each t-object. Here K is an input parameter fixed by the application programmer depending on the requirement. Our algorithm is dynamic which can support different values of K ranging from 1 to infinity . If K is infinity then there is no limit on the number of versions. But a separate garbage-collection mechanism is required to collect unwanted versions. On the other hand when K is 1, it becomes same as a single-version STM system. We prove the correctness and starvation-freedom property of the proposed KSFTM algorithm. To the best of our knowledge this is the first multi-version STM system that is correct and satisfies starvation-freedom as well.