If he's not a cleric, call the ghostbusters.
Give him a "blessed" weapon, or have a priest bless the weapon to be used. Or provide a "special" weapon that was crafted specifically to kill these ghosts that doesn't necessarily have the +1 bonus, but can be used against undead successfully. Or have him sprinkle holy water on his weapon.
If you're the DM you should be providing SOMETHING he can use; it might be a weapon, it might be knowledge, it might be the ability to do something the ghosts cannot do themselves. If not, then you need to make sure he knows he doesn't have the tools to take on these ghosts and he should turn around and fight other critters for a while longer.
You say you don't want to destroy them?! A powerful cleric might banish them, or successfully turn them. If your fighter has no magic items, it's time for him to find help.
You dont' provide enough details for anybody to help you very much. If the fighter doesn't have the resources to fight ghosts, he should know enough to run away and not mess with them, at least in a fight. Maybe he can talk to them, or manipulate them by performing a favor for them. Ghosts usually want something besides just to hang out. There is usually a reason they stayed behind--what is it?
This is where role-playing can take place. Think about the motivations for all individuals involved. What do they want, what do they fear, what do they get upset or angry about? You need to do this for all your villains and NPCs!
**edited to cut out my smart comment about the person not actually having an idea in the first place**
(Ahh, to be a young DM)