Please provide more details about this. How old is your computer? Were you using another Anti Virus program prior to Avast ? What is showing in your Security Centre & has this changed? What other security progs are you running? Are you able to update Avast? Are automatic updates turned on? etc.etc.
I think mine shows the same thing. Under the Security Tab in Control Panel, it says I do not have any anti-virus, but I can see the Avast icon globe at the bottom of the screen spinning, so I think it is actually working....