Problem statement: As grid resources are geographically distributed, efficient resource discovery and management has become one of the important requirements. Besides, Grid users are independent identities and negotiation is necessary for reconciling their diverse characteristics. Therefore special mechanism was required to negotiate and discover the required resource or similar resource as an alternative when discovery fails. Moreover the quality of the service being provided in the grid environment depends on both functional as well as the Non-Functional Requirements [NFR]. But conflicts between NFRs are not yet resolved effectively. Discover the requested resources to the requester, Provide compromised alternate resources by negotiation when resource discovery fails to increase the success rate of the agent, Provide knowledge for efficient management of resources and quality of service is to be improved by considering NFR. Approach: A system Agent Based Grid Resource Discovery with Negotiated Alternate Solution and Non-Functional Requirement Preferences (AGRD_NFRP) was proposed to provide an expeditious resource and most relevant alternate resource when discovery fails. Four types of intelligent and mobile agents were proposed for judicious management of resources to the advantage of resource providers and requesters in ensuring speedy execution of processes. Resource discovery, negotiation and alternate solution were handled by these agents. In order to improve the quality of the service the non-functional requirements of the grid user request with their preferences were identified and conflicts among them were analyzed using fuzzy rules. Results: The results showed that the AGRD_NFRP system proposed is producing consistently higher success rate by providing alternate solution and getting knowledge from the cognitive agent. Quality of the service was enriched by prioritizing the preferences of grid user. Conclusion: On numerous occasions, grid users face non availability of high-end resources for completing the task on hand. In this context, the approach outlined in this research is most appropriate, convenient and efficient. The AGRD_NFRP system proposed herein played a crucial role in bridging the seemingly wide gape between resource requester and resource owners.