Recently, the implementation of rectangular waveguides for generation and manipulation of orbital angular momentum (OAM) modes, has been developed to exploit the outstanding features of these modes in more complex integrated devices. Multimode interference (MMI) structures have been widely used in both one and two dimensions as the basic elements in many integrated optical devices like optical beam splitters, mode converters, couplers, wavelength-division (de)multiplexers, and switches. According to the various applications of OAM modes in quantum and classical communications, the study of their propagation properties in MMI waveguides is useful in order to facilitate the way into higher security and capacity systems. In this work, mode conversion between beams carrying OAM with opposite topological charges in the two-dimensional (2D) MMI waveguides is investigated. In this investigation, the OAM modes with odd topological charges are considered. Using the self-imaging properties of MMI structures, an integrated device including two MMI waveguides connected by phase shifters and linear waveguides is designed. The design procedure is performed for OAM modes with topological charge values of l=±1 and l=±3 using beam propagation method. The proposed device is passive with reciprocal behavior and has the output mode purity of 94% and 82% for beams carrying l=±1 and l=±3, respectively.