We propose and demonstrate the inscription of parallel long-period gratings (LPGs) in a few-mode fiber (FMF) using femtosecond lasers. Mode conversion from the fundamental (LP01) mode to high-order core modes, including LP11, LP21, LP31, LP02, and LP12, is achieved by controlling the inscription period of the gratings. Taking advantage of the highly focused femtosecond laser, LPGs with different off-axis offsets were fabricated, and the resonance wavelength and the inscription efficiency of the gratings versus the offset were investigated. Based on the off-axis writing technique and using the femtosecond laser source, we wrote parallel LPGs that contain multi-gratings in a single FMF and achieved a multi-channel core mode converter in a single FMF with flexibility in terms of the resonant wavelength and mode conversion among different modes. This approach offers a new, to the best of our knowledge, option for implementation with high integration, and a multi-channel mode converter, which could find potential applications in FMF multi-wavelength laser systems, and wavelength/mode division multiplex communication systems. Furthermore, these microstructured LPGs integrated into an optical fiber can be used as a multifunctional sensor.