Yes, you have to be good at both, especially science.
Isn't psychology a science? It deals with the study of behavior, both in humans and animals, and therefore interrelates with other disciplines like philosophy, biology, and sociology.
How can you become a psychologist if you are not good in science? You need to understand and know our bodily functions, especially neurological ones, and there is chemistry involved in that!
You do need math. I'm pretty sure you're going to take some math courses like psychological statistics. But, you won't need it THAT much. You'll need to tally lab results, and calculate descriptive statistics such as mean, median, mode, standard deviation and correlation.
Etc...Hope that helps. ;)