How long should a fully charged battery last for a gateway laptop model mx6446. After an hour my battery needs to be recharged.

Depends on what your doing with it.
Example:
Your running the screen on "full" bright mode and not reduced mode. Your using WiFi at the same time downloading (which is powering the diskdrive) and your also listening to music as you do all this.

That can suck the life out of a battery quick. Also depending on the age and type of battery it may not have full power to charge to.

With taking in consideration of above

You should also take advantage of power settings through control panel where you can change settings that use less power when in battery mode. Depending on your model, the laptop itself may have it's own settings option for battery powered preferences.

Can be anywhere between the hour you have now to around 2-2.5 hrs depending on power consumption while using battery. New laptops are about 2-2.5 hrs.

What's the age of the battery?

Has the battery gas gauge been calibrated?