Most likely you need to replace the battery. Open System Information in the Utilities folder. Click on the Power entry in the Hardware list. You should see a display showing your batteries stats (be sure not to have the charger connected.) If you see that the battery needs replacing then that's what you need to do. You can check at OWC to see if they have a replacement battery kit for your model.
If the battery is OK and does not have more than 1,000 charges, then you may have a motherboard problem: Make an appointment at the Apple Retail Store - Genius Bar for service. If needed find an Apple Store - Find a Store - Apple.