Dementia is an illness that causes memory problems; changes in behavior; and difficulty with thinking, making decisions, and carrying out daily activities. Many people with dementia also have anxiety, and yet very little is known about effective treatment strategies for anxiety in this population. Cognitive behavioral therapy (CBT) is a type of psychotherapy that is commonly used to treat anxiety. CBT involves teaching patients skills to help them manage their anxiety, such as relaxation, changing their thoughts, and problem-solving. This study will evaluate the effectiveness of CBT in treating anxiety in older adults with dementia. In addition, the study will determine the effect of the treatment on patients' families and friends, and how families and friends may be able to help patients manage their anxiety. All study participants will name a family member or friend who will also participate in the study.