The ionic bonding across the lattice and ordered microscopic structures endow crystals with unique symmetry and determine their macroscopic properties. Unconventional crystals, in particular, exhibit non-traditional lattice structures or possess exotic physical properties, making them intriguing subjects for investigation. Therefore, to accurately predict the physical and chemical properties of crystals, it is crucial to consider long-range orders. While GNN excels at capturing the local environment of atoms in crystals, they often face challenges in effectively capturing longer-ranged interactions due to their limited depth. In this paper, we propose CrysToGraph ($\textbf{Crys}$tals with $\textbf{T}$ransformers $\textbf{o}$n $\textbf{Graph}$s), a novel transformer-based geometric graph network designed specifically for unconventional crystalline systems, and UnconvBench, a comprehensive benchmark to evaluate models' predictive performance on unconventional crystal materials such as defected crystals, low-dimension crystals and MOF. CrysToGraph effectively captures short-range interactions with transformer-based graph convolution blocks as well as long-range interactions with graph-wise transformer blocks. CrysToGraph proofs its effectiveness in modelling unconventional crystal materials in multiple tasks, and moreover, it outperforms most existing methods, achieving new state-of-the-art results on the benchmarks of both unconventional crystals and traditional crystals.