You either 'raise' or 'bring up' children. Both are possible and have the same meaning. 'Raise' tends to be used more in the USA. 'Raise up' doesn't really exist in this context.

You should say "Bring up children." to mean to care for the children up to their adulthood, being their parents or guardian. Or, you can say "Raise children.", which, too, has the same meaning as the above sentence. But saying "Raise up children" will, rather, mean to lift them up. (Raise Up means to lift someone/ something up.)

Additionally: an OBSOLETE detail. a) When I was a child, teachers sometimes said "you raise animals, you rear children." That is, it was inappropriate to use the word "raise" to refer to children. This distinction is no longer observed.