In the previous study, the authors showed the results that the cycloid gear pair with tooth number difference of two does not only increase the contact ratio and decrease the maximum shared load of the individual contact tooth pair, but also reduce the bearing loads of the cranks slightly. However, stress concentration occurs on the tip segment of cycloid teeth, if no suitable flank modification is available. The aim of the paper is to propose a new design approach for flank modification of cycloid profile to improve the contact characteristics. Besides the conventional methods for flank modification, i.e. equidistant offset and shifting offset modification, a new flank modification with multiple variables, so-called free profile modification, is proposed in the paper. Only the cycloid planetary stage with two cycloid discs are considered in the study to simplify the analysis. Two analysis approaches, tooth contact analysis and loaded tooth contact analysis, are developed for evaluation of the modified profile accordingly. A method based on the geometrical property of cycloid profile, named “tracing circle method”, is employed to determine exactly the contact points and the other kinematic characteristics of drives. The developed LTCA approach based on the influence coefficient method is used to calculate the contact stress of the modified cycloid tooth pair with considering the stiffness of supporting bearings and the influence of the eccentric error of the cycloid disc. The variation of shared load, the contact stress, the bearing load and the torque distribution are analysed in the paper to evaluate the various flank modification methods. Some useful design guidelines, summarized from the systematic analysis results, are also given in the paper.