A question about credit scores?

If i open a sears or lowes credit card and get a line of credit for $2000 and spend that $2000. If i make about 6 months of ONTIME payments and then pay it off and at the same time cancel the credit card, will that hurt my credit for canceling the credit card. Im asking cause i was told that it would hurt my credit score cause it dosent look good. I thought if you paid something off that meant a good thing and didnt know that canceling a credit card would hurt your credit. Ive never heard of that...Please tell me thats not true