I'm going out with a guy for almost a year; he just told me he wasn't honest with me. He said that He was seeing someone before, but he end it up before we got serious. I know they saw each other while we were together, I know she has strong feeling for him. Now they keep in touch here and there sometimes. He assures me nothing happened between them, that this is the present and that we are together and happy. I should trust him?

Do you have any reason not to trust him?
If the answer is no then I would just go with it as it is possible he is being completely honest. If it bothers you he still sees this girl then tell him maybe you could meet her too with him to put your mind at rest.
Try not to question him too much though if you do trust him as this will just make him feel you don't trust him and could create problems that could be avoided. Hope this helps