Is it normal for my baby to eat more at night than during the day?

Yes. Some babies, particularly those who were more active in the womb at night may have their circadian rhythm reversed and will be more active and hungry at night. As the baby becomes more interactive with the environment this usually changes. If this pattern is persistent I recommend the parents move to a more appropriate time zone (just kidding!).
Day night reversed. Wake the baby from naps before his is ready to wake, and feed him each time. When he wakes at night, don't feed him fully. If you decrease calories at night, he will take more in the day. Warning - it can take 4 to 6 weeks to reverse his pattern, and many nights with interrupted sleep.