We investigate the nonlinear frequency conversion of non-diffracting optical modes via non-degenerate four-wave mixing(FWM) process in rubidium vapor. In this process, two strong control fields and a weak probe field mutually interact via afour-level double-Λ type atomic system to produce a new frequency weak Stokes field which is a phase conjugate to probe. We show that any arbitrary mode such as Airy, Bessel, Mathieu, and Weber beams encoded initially in the spatial envelope of probe field are efficiently transferred to FWM Stokes field by satisfying the phase matching condition. Interestingly, we found that the transmitted intensity profiles of Stokes beam are identical to that of probe beam while phase profile is complimentary.The phase conjugation property of output beams is revealed by interfering them with a copropagating plane wave. We further found the fidelity in terms of structural similarity between two transmitted modes of about 99%, which substantiates the high efficiency of FWM process. The efficient transfer and frequency conversion of such diffraction-free beams may have potential applications in nonlinear optical and quantum technologies.