A photon pair can be entangled in many degrees of freedom such as polarization, time bins, and orbital angular momentum (OAM). Among them, the OAM of photons can be entangled in an infinite-dimensional Hilbert space which enhances the channel capacity of sharing information in a network. Twisted photons generated by spontaneous parametric down-conversion offer an opportunity to create this high-dimensional entanglement, but a photon pair generated by this process is typically wideband, which makes it difficult to interface with the quantum memories in a network. Here we propose an annual-ring-type quasi-phase-matching (QPM) crystal for generation of the narrowband high-dimensional entanglement. The structure of the QPM crystal is designed by tracking the geometric divergences of the OAM modes that comprise the entangled state. The dimensionality and the quality of the entanglement can be greatly enhanced with the annual-ring-type QPM crystal.