Yes, your new battery is probably working fine. However, until you calibrate it, the battery monitor on the iPhone cannot get an accurate reading of the battery's charge status; it doesn't know the range from full to empty.
To calibrate it, run the battery down to below 5% (or as low under that as you can bear). Then, plug it in to charge - but don't use it while it's charging and don't take it off the charger until it's at 100%. This way, again, the battery monitor know where completely empty is versu completely full and so can show you an accurate battery percentage.
Marilyn