According to Fuji, 32 GB SDHC card should work with this camera.

However:

• The card must be formatted in the camera before the camera can use it. For the correct formatting procedure, see p. 99 of the user manual. If you don't have the user manual get it here: http://www.fujifilm.com/support/digital_...
• SDHC cards can be write-protected. They have a little tab on the left edge (looking at the label side with the label text right side up) - if the tab is in the LOCK position the card cannot be formatted and data cannot be written to the card. Use your fingernail to move the tab to the unlocked position.
• Beware of counterfeit memory cards. Cheap chinese knock-offs are available that look just like the real thing but are of inferior quality and often do not meet their stated capacity or speed rating. In some devices such cards may not work at all.