We study a quantum few-mode fiber (FMF) communication scheme based on orbital angular momentum (OAM) modes and applied quantum information theory to develop the quantum FMF channel model and to calculate the quantum channel capacity. We assume a strong mode-coupling regime in FMF and an imperfect generation of OAM modes. The quantum FMF channel is modeled as a concatenation of many fiber sections describing the OAM eigenkets transitions as a Markov chain. The proposed model is suitable for the study of the multidimensional quantum key distribution and teleportation over FMFs. Numerical simulations are performed to demonstrate the ability of the model to determine the FMF output density state for a given input density state. It is shown that FMF quantum channel capacity decreases with distance in a strong coupling regime if OAM basekets are imperfectly generated.