Mode-division multiplexing (MDM) is a promising technology for increasing the data-carrying capacity of a single few-mode optical fiber. The flexible mode manipulation would be highly desired in a robust MDM network. Recently, orbital angular momentum (OAM) modes have received wide attention as a new spatial mode basis. In this paper, we firstly proposed a long period fiber grating (LPFG) system to realize mode conversions between the higher order LP core modes in four-mode fiber. Based on the proposed system, we, for the first time, demonstrate the controllable all-fiber generation and conversion of the higher order LP core modes to the first and second order circularly polarized OAM beams with all the combinations of spin and OAM. Therefore, the proposed LPFG system can be potentially used as a controllable higher order OAM beam switch and a physical layer of the translating protocol from the conventional LP modes communication to the OAM modes communication in the future mode carrier telecommunication system and light calculation protocols.