Unfortunately, it is very normal. Submission to dmoz can take more than a year. You read that correctly. Sometimes it only takes a few months but more often than not, it takes longer.

To submit to dmoz, make certain you read the submission guidelines thoroughly and that your submission and website complies fully. Submit your site. Forget about it.

If your site meets all of the guidelines then it will eventually get included in the directory. If it doesn't meet the guidelines or you have submitted it to the wrong category, then it will either be rejected for non-compliance or it will be put to the back of the queue for the correct category which can stretch the time for it to get through the submission process considerably.

Don't keep resubmitting your site. This is viewed as spamming the submission process and can get you rejected outright.