The predominant grid authentication mechanisms use public key infrastructure (PKI). Nonetheless, certificate-less public key cryptography (CL-PKC) has several advantages that seem to well align with the demands of grid computing. Security and efficiency are the main objectives of grid authentication protocols. Unfortunately, certificate-less authenticated key agreement protocols rely on the bilinear pairing, that is extremely computational expensive. In this paper, we analyze the recently secure certificateless key agreement protocols without pairing. We then propose a novel grid pairing-free certificate-less two-party authenticated key agreement (GPC-AKA) protocol, providing a more lightweight key management approach for grid users. We also show, a GPC-AKA security protocol proof using formal automated security analysis Sycther tool.