The improved symbiotic organisms search (R-SOS) Algorithm is proposed to estimate parameters of smooth and non-smooth fuel cost functions for improving the solution accuracy of economic dispatch problems. Determining accurately of fuel cost curve is a crucial task, because they effect directly solution accuracy of economic dispatch and optimal power flow problems. There are two models as smooth and non-smooth forms to describe the input-output characteristics of generators in thermal power plants. This paper presents an implementation of the R-SOS algorithm in order to estimate parameters of these functions. First, second and third order smooth fuel cost functions and non-smooth fuel cost function with valve point effects are used in the study. The estimation problem is described as an optimization one. The R-SOS algorithm is proposed for solving this optimization problem and it minimizes the total error of estimated parameters. The performance of the R-SOS algorithm is tested on four different cases having different fuel types. Results obtained are compared to classical Symbiotic Organisms Search and other meta-heuristic methods and they show that the proposed R-SOS algorithm is favourite model in all test cases for estimating accurately of fuel cost function parameters.