If the order is not important, you should use set.difference. However, if you want to retain order, a simple list comprehension is all it takes.
result = [a for a in A if a not in subset_of_A]
EDIT: As delnan says, performance will be substantially improved if subset_of_A is an actual set, since checking for membership in a set is O(1) as compared to O(n) for a list.
A = [6, 7, 8, 9, 10, 11, 12]
subset_of_A = set([6, 9, 12]) # the subset of A
result = [a for a in A if a not in subset_of_A]