Exam anxiety can be a real tough obstacle to overcome. At it's root, I believe, is the stress that comes from feeling the pressure to do well in an unpredictable situation for which you do not feel prepared.
You can reduce that stress by attacking all elements of the problem.
First is the pressure to do well. Of course you want to do well, but sometimes it can help to set specific and realistic goals for yourself. This gives you something tangible to aim for rather than the unrealistic "being perfect." The most obvious example here is aiming for a certain grade, but that doesn't always have to be the only goal. Maybe you want to master a certain skill. Once you have a specific goal you can develop a plan for moving towards it. This helps to reduce your stress because it puts a little more control over the situation in your hands.
Second is the unpredictability of the situation. One big tip here is to look up the exams from previous years. Libraries usually archive these. You can usually find examples online as well. I usually tried to work my way through at least one or two "sample" exams prior to writing the exam. If you do enough of them, you begin to see patterns in the questions. The specific parameters will of course change year to year and occasionally the professor will insert something completely new, but if you can comfortably answer all of the problems on the last three exams, you're not likely to be too tripped up when you write the current one.
Another approach to this is to ask yourself what questions you would put on the exam if you had to make it up as a professor. You know what time frame the students will have. You know what's been covered and you likely want to cover as much of the syllabus as you can.
Finally that last point - feeling unprepared - has no "secret" solution. You reduce that element of anxiety by preparing. Organizing your time helps in this regard. Knowing that you've put in a certain amount of hours into preparing for an exam can boost your confidence. And if you're not seeing the results you want, try increasing this. One trick I used to do was to keep all of my study notes and then the last thing I would do before going to an exam was to count the pages. This helped calm my nerves because it was a tangible reminder of the work I had put into prepare for the exam.