Create smooth animation in path finding

I have written algorithm of path finding and it works nicely. For this following tutorial help me a lot : Introduction to A* Pathfinding

In this, I am moving my main player tile per tile towards target. But it creates very poor animation.

I have used following code for this purpose.

 private void MoveToNextWayPoint(int waypoint)
         {
                 if (waypoint < closedList.Count)
                 {
                         iTween.MoveTo(playerAObject, iTween.Hash("x", closedList[waypoint].transform.position.x, "y", closedList[waypoint].transform.position.y,
                                 "time", 0.25f, "easetype", iTween.EaseType.linear, "oncompletetarget", gameObject, "oncomplete",
                                 "MoveToNextWayPoint", "oncompleteparams", waypoint + 1));
                 }
         }

Basically I want to say that player stop at one time and start travelling for next tile. So that this movement looks very poor experience.

I want your help to make this correct. If you want any more information then ask me.