The generation of orbital angular momentum (OAM) modes is very important, for they have a variety of applications such as in optical tweezers, quantum optics, and optical communication systems. Particularly, how can high-order OAM modes be generated efficiently in fibers with the advantage of low cost and compatible with fiber system? The Traditional method for first order to third order OAM is based on long period fiber grating (LPFG) fabricated by carbon dioxide laser. However, high power and large focused spot of carbon dioxide laser are unfavorable for stable and repeatable generation of higher-order OAM, which needs the LPFG with small grating pitch. In order to solve this problem, a third-order OAM mode converter based on femtosecond microfabrication is proposed and fabricated for the first time. With the advantage of 4.4 μm focused spot size near the core, lower power and lower heat absorption efficiency, this method can be more stable and promising. Therefore, we first carry out the mode filed analysis and simulate the intensity and phase profiles of the superposed mode field in LP odd-even mode on different scales and phases patterns to obtain OAM mode. Second, we use the coupled-mode theory to analyze and simulate the transmission spectrum of LPFG, which guides the setting of the grating parameters such as the grating pitch, the depth of modulation and the length of the grating. By experimental verification, an asymmetric modulated long-period fiber grating with a pitch setting to 194 μm is fabricated on a six-mode fiber. The fundamental mode can be converted into the third-order angular linear polarization mode LP₃₁ mode with 98% mode conversion efficiency near 1550 nm, and further converted into the OAM_±3 modes by superposition of the odd and even LP₃₁ mode with ±π/2 phase difference. At the same time, this fiber grating can also generate LP₁₂ mode with 90% mode conversion efficiency near 1325 nm. Then we can take the same approach to transform LP₁₂ mode into OAM modes with angular first-order as well as radial second-order. The experimental result is consistent with the simulation result. Thus, this scheme provides an idea for generating the high-order OAM modes in all-fiber systems by using only one grating with high repeatability.