Website shifting

Question

I have a website on a server but we are not satisfied with the services from them.
so we bought a new domain and space on godaddy and transfer our site to godaddy.

now what I want when user enter the old url it should show the content of new domain. i dont want to change the domain name (url forwarding). In address bar my old domain name should come but content should come from the new domain.

Is it possible.