Do you have a meter? If so, your converter should be outputting 13.6 volts or so with no battery connected. You want to put one test lead on the positive (+) connection and one test lead on the negative (-) connection.
To accurately test the converters output, a battery or load should be connected to it and amperage should be measured. The converter may start in bulk mode at 14-14.8 volts with a large amount of amperage, then go into absorb mode. In absorb mode amperage will lessen as the battery becomes charged. The final mode is float and that should be low amps with voltage around 13.6 or less volts.
As was posted previously, if you will state what brand and model of converter you have, you'll get some better advice. Some converters have known issues and if you have one of them, you'll want to replace it.