The core goal of resource management is to establish a mutual agreement between a resource producer and a resource consumer by which the provider agrees to supply a capability that can be used to perform some tasks on behalf of the consumer. Market-based approaches introduce money and pricing as the technique for coordination between consumers and producers of resources. In this paper, we propose a market-based mechanism to allocate computational resources (CPU time) with a single central Market in a local Grid. In such a network whenever any node can offer idle CPU time to the Grid and whenever a node has some tasks waiting for free CPU, it may request the resource from the Grid. In our approach, consumers and producers are autonomous agents that make their own decisions according to their capabilities and their local knowledge. Continuous Double Auction model is used as a technique using which these selfish agents can coordinate their work and make their decision. The performance of this mechanism is evaluated and is compared with the simple FCFS mechanism.