In this study participants will be asked to participate in a training study to examine whether a new walking intervention that combines cognitive training with walking on a treadmill improves walking more than gait training or cognitive training alone. Participants with Parkinson's disease (PD) will come to the lab for a complete gait assessment using a motion analysis system that will record leg motion and muscle activity during comfortable walking. During the initial evaluation, participants will also complete cognitive assessments and surveys about community activities and quality of life related to PD. Participants will be divided into one of the three training groups and asked to come to the lab three times a week for four weeks during the intervention. One week and one month after training, participants will return to the lab to complete all the same assessments that were performed during the initial visit. The results of the three testing sessions (initial, one week and one month) will be compared between and within groups to see if any of the interventions provided unique benefits to the health of persons with PD.