A two-core optical fiber composed of a single-mode core and a few-mode core is proposed. Index-matched coupling between two fundamental modes in two cores can be achieved by applying a long-period fiber grating in the few-mode core. Mode-field conversion between the small mode-field area and the large mode-field area with low loss can be achieved by this configuration. Numerical simulation shows that the operation bandwidth of the mode-field converter can be as large as 36 nm if the insertion loss of the converter should be lower than 0.5 dB. Results show that this structure has higher conversion efficiency and lower cross talk as compared to the scheme of direct connection between the single-mode fiber and the few-mode fiber.