You have misunderstood. The traveller is travelling at close to the speed of light for a year and his on-board clock will tell him he's been travelling for a year. But time does not slow down for him only to an outside observer does it appear to slow down.

The observer will have seen that the traveller is travelling at nearly the speed of light for a year and so will also see from his clock that they have travelled nearly a light year.

From both frames of reference a light year is travelled but their clocks will show quite different results. The velocity will always have remained constant.

How is that possible you ask????

It is possible because you are incorrectly trying to use the simple "distance/time = speed" equation which doesn't work at speeds close to the speed of light. Space and time are not absolute quantities but differ from different reference points and at different (very high) velocities. You have to use a different equation called a  a Lorentz transformation for objects travelling at or near the speed of light to resolve this sometimes confusing anomaly. Wiki it to find out what that is.