We demonstrate the fabrication of high-quality LPFGs in simplified hollow-core photonic crystal fibers, composed of a hollow hexagonal core and six crown-like air holes, using CO2-laser-irradiation method. Theoretical and experimental investigations indicate that the LPFGs are originated from the strong mode-coupling between the LP01 and LP11 core modes. And a dominant physical mechanism for the mode-coupling is experimentally confirmed to be the periodic microbends rather than the deformations of the cross-section or other common factors. In addition, the LPFGs are highly sensitive to strain and nearly insensitive to temperature, and are promising candidates for gas sensors and nonlinear optical devices.