I need suggestions on what I can do for a literary analysis of Beowulf, perhaps comparing Anglo-Saxon culture to ours.

One component of literary analysis is a discussion of
setting, so a discussion of the Anglo-Saxon culture as revealed in Beowulf
would certainly be appropriate, enlightening and interesting. Expanding that
discussion by comparison to contemporary society would be equally appropriate and valid.
Unless you are doing an extensive paper of around 5,000 or so, you may want to narrow
your focus down to one aspect of Anglo-Saxon culture revealed in
Beowulf.

For instance, you might
easily examine the relationship between the male warriors and compare that to male
relationships, as you perceive them, today (e.g., Do males today form friendships of
equality and mutual benefit?). You might examine the relationship between the leader and
his lieges and compare it to a corporate or government structure of today (e.g., Do
leaders of today reward loyal followers and bestow gifts on them to honor them?) You
might examine the clout and authority of the women in Beowulf and
compare that to the clout and authority women carry today (e.g., Do men do as a woman
asks just because she asks it today? Do women have the authority to bestow rewards and
honors upon men today?)