The paper proposes a novel constraint handling technique to improve the efficiency with Genetic Algorithms, which could effectively attack the problem of economic-environmental power dispatch (EED) under the constraint of generation rate. EED is a sophisticated and difficult task because of the conflicting requirements of minimising generation cost and reducing environmental pollution. The problem is made even more formidable with the additional constraint of generation rate. Genetic Algorithms (GAs) are a promising approach to solving the highly constrained multi-objective problem involved in the solution. However, the performance is affected crucially by the way a constraint is handled in the GA-implementation. The conventional method, which passes only a constraint equation to the fitness function, exhibits great difficulties for a GA to reach the global optimum. In this paper, the proposed constraint handling method incorporates the concept of how far a solution is away from the feasible region so as to improve the genetic search ability. To enhance the GA performance further, the paper also employs a unique fitness function formulation alongside the proposed constraint handling technique. The modified GA is applied to the highly constrained EED problem on a four generator system. The study shows that the proposed distance based constraint handling is performed better than the conventional equation based method, and could provide easy and efficient means to attack the difficult problem presented by economic-environmental dispatch.