Cloud Computing service is the next gigantic concept for both computation and business policy. Cloud service is the most efficient service of modern day. The vast power as well as the unlimited space at the most effective cost makes this service to hold the top position of modern world business. At the same time huge computation is available through Cloud service, is just in reach of hand. I here try to find out the performance of Cloud Computing. I choose Google App Engine as the cloud service provider. On the cloud environment I implement the Traveling Salesman Problem and try to solve it using Genetic Algorithm. The same implementation has been used for Desktop environment. Based on the result of two different environments I reach on the decision that, Cloud service is much faster than the desktop environment.