Analogous to single-mode fiber, nonlinear effects may eventually limit the information capacity in next generation long-haul few-mode fiber (FMF) transmission systems. In this paper, we theoretically and numerically investigate inter-modal four-wave mixing (IM-FWM) among up to four spatial modes in FMFs. Different forms of multi-mode non-linear Schrödinger equation (MM-NLSE) for two, three and four spatial modes are derived, along with up to six types of wave/mode distributions and their corresponding phase matching conditions. We analyze the mixed effects of differential mode group delay (DMGD), chromatic dispersion (CD), random mode coupling (RMC) and wavelength separation upon IM-FWM efficiency in FMF.