In this article, the modified exponential function method is applied to find the exact solutions of the Radhakrishnan-Kundu-Lakshmanan equation with Atangana’s conformable beta-derivative. The definition of the conformable beta derivative and its properties proposed by Atangana are given. With the proposed method, exact solutions of the nonlinear Radhakrishnan-Kundu-Lakshmanan equation which can be stated with the conformable beta-derivative of Atangana are obtained. The exact solutions found as a result of the application of the method seem to be 1-soliton solutions, dark soliton solutions, periodic soliton solutions and rational function solutions. According to the obtained results, we can say that the Radhakrishnan-Kundu-Lakshmanan equation with Atangana’s conformable beta-derivative have different soliton solutions. Also, three-dimensional contour and density graphs and two- dimensional graphs drawn with different parameters are given of these new exact solutions.