Recent studies have shown that introducing metal elements into nitrogen matrix can induce more stable poly-nitrogen structures than the pure nitrogen phase due to the ionic interaction between metal elements and nitrogen matrix. Many types of poly-nitrogen structures have been reported by using the alkaline earth metal elements (M = Be, Mg, Ca, Sr, Ba) as the coordinate elements. For example, the one-dimensional (1D) infinite armchair poly-nitrogen chain (N_∞) structure and N₆ ring structure are obtained for the MN₄ and MN₃ chemical stoichiometry, respectively. Interestingly, the stabilities of theses MN_x structures are enhanced 2–3 times compared with that of the pure nitrogen. Therefore, exploring the novel and stable poly-nitrogen structure by introducing alkaline earth metal elements under high pressure is a great significant job. As an alkaline earth element, Ca is abundant in the earth. Its ionization energy (I₁ = 590 kJ/mol) is far lower than that of Be (900 kJ/mol) and Mg (738 kJ/mol), which means that Ca can form calcium nitrides more easily. Zhu et al. (Zhu S, Peng F, Liu H, Majumdar A, Gao T, Yao Y 2016Inorg. Chem. 55  7550) proposed that the Ca-N system can obtain poly-nitrogen structures under high pressure, such as CaN₄ structure with armchair nitrogen chain, CaN₅ and CaN₃ consisting of pentazolate “N₅” and benzene-like “N₆” anions. These poly-nitrogen structures have potential applications in the field of high energy density materials. Here, we report the prediction of Ca-N system at 100 GPa by using particle swarm optimization algorithm technique for crystal structure prediction. A new thermal stable phase with P 2₁/c-Ca₅N₄ space group is found at 100 GPa, which enriches the phase of Ca-N system under high pressure. The dynamic stability and mechanical stability of new phase are confirmed by phono dispersion spectrum and elastic constant calculations. The electron localization function analysis shows that the nitrogen atoms in P 2₁/c-Ca₅N₄ are bonded by N—N single bond and electron transfer from Ca atom to N atom enables Ca₅N₄ to serve as an ionic-bonding interaction structure. Band structure calculation shows that the Ca₅N₄ has a semiconductor structure with a direct band gap of 1.447 eV. The PDOS calculation shows the valence band near Fermi energy is mainly contributed by N_p electrons, while the conduction band is mainly contributed by Ca_d electrons, indicating that electrons are transferred from Ca atom to N atom. Bader calculation shows that each N atom obtains 1.26e from Ca atom in P 2₁/c-Ca₅N₄. The Raman spectrum and X-ray diffraction spectrum are calculated and detailed Raman vibration modes are identified, which provides theoretical guidance for experimental synthesis.