In this work, we have proposed yet another forward secure signature based on bilinear pairings. Our forward secure signature requires the general security parameters only independent to the total number of time periods. The scheme can perform key evolving for unlimited time periods while maintaining sizes of keys and signature fixed. In addition, the signing algorithm is very efficient with the simple verification algorithm. We also provide a formal definition along with a detailed security proof of our signature scheme under the assumption of Computational Diffie-Hellman problem.