In this paper, a one rank cuckoo search algorithm (ORCSA) is proposed for solving economic load dispatch (ELD) problems. The main objective of the ELD problem is to minimize total cost of thermal generators while satisfying power balance constraint, prohibited operating zones, ramp rate constraints and operating limits of generators. Moreover, the generating units considered in this paper have different characteristics such as quadratic fuel cost function, nonconvex fuel cost function and multiple fuel options. The proposed ORCSA method has been developed by performing two modifications on the original cuckoo search algorithm (CSA) to improve optimal solution quality and computational time. The first modification is to merge new solution generated from both Lévy flights and replacement a fraction of egg together and to evaluate and rank the solutions at once only. A bound by best solution mechanism has been used in the second modification for properly handling the inequality constraints. The proposed ORCSA method has been tested on different systems with different characteristics of thermal units and constraints. The results obtained by ORCSA have been compared to those from other methods available in the literature and the result comparison has indicated that the ORCSA method can obtain better solution quality than many other methods. Therefore, the proposed ORCSA can be a very effective and efficient method for solving ELD problems.