The absence of nesting between electron and hole pockets in LiFeAs with Tc=18 K attracts great attention, as an important hint to understand the pairing mechanism of Fe-based superconductors. Here, we study the five-orbital model of LiFeAs based on the recently developed orbital-spin fluctuation theories. It is found that the experimentally observed gap structure of LiFeAs, which is a “fingerprint” of the pairing mechanism, is quantitatively reproduced in terms of the orbital-fluctuation-mediated s++-wave state. Specifically, the largest gap observed on the two small hole pockets composed of (dxz,dyz) orbitals can be explained, and this is a hallmark of the orbital-fluctuation-mediated superconductivity. The s++-wave gap structure becomes more anisotropic in the presence of weak spin fluctuations. As the spin fluctuations increase, we obtain the “hole-s±-wave state,” in which only the gap of the large hole pocket made of the dxy orbital is sign reversed, due to the cooperation of orbital and spin fluctuations. This gap structure with “sign reversal between hole pockets” is similar to that recently reported in (Ba,K)Fe2As2.