Praise be to Allah.
There is nothing wrong with dyeing your hair brown even if you do not use henna. What is not allowed is to dye one's hair black, because of the hadeeth narrated from the Prophet (peace and blessings of Allaah be upon him) (see question #261 ).
Similarly it is not permitted to dye one's hair in a manner that imitates the kuffaar, like the "punks" why dye their hair in all kinds of colours. We ask Allaah for safety and health.