Predicting properties of crystals from their structures is a fundamental yet challenging task in materials science. Unlike molecules, crystal structures exhibit infinite periodic arrangements of atoms, requiring methods capable of capturing both local and global information effectively. However, current works fall short of capturing long-range interactions within periodic structures. To address this, we leverage \emph{reciprocal space}, the natural domain for periodic crystals, and construct a Fourier series representation from fractional coordinates and reciprocal lattice vectors with learnable filters. Building on this, we introduce the reciprocal space-based geometry network (\textbf{ReciNet}), a novel architecture that integrates geometric GNNs and reciprocal blocks to model short-range and long-range interactions. Experiments on comprehensive benchmarks JARVIS, Materials Project, and MatBench demonstrate that ReciNet achieves outstanding predictive accuracy across a range of crystal property prediction tasks. Additionally, we explore a model extension for multi-property prediction with the mixture-of-experts, which demonstrates high computational efficiency and reveals positive transfer between correlated properties. These findings highlight the potential of our model as a scalable and accurate solution for crystal property prediction.