The certificate is a central concept in Grid Security Infrastructure authentication. The certificate guarantees the authenticity of the data, thus effectively authenticating the sender. In this paper, we propose a secure certificate authentication framework using Counting Process to interact trusty for Grid users .We intend to apply this approach in secured performance on Grids as well as in grid application for authenticating users, protecting attacks, and recovering failed systems. The main idea presented in this paper is to add counting process and matching method into RSA algorithm to apply in Grid certificate authentication.