This paper proposes a curved link-slab (CLS) structure, simplified into a hingeless-arch model, to address the current cracking phenomenon of CLS concrete. The stress formula of the hingeless arch under various loads is derived based on the classical mechanic's method. Based on an actual bridge example, the mechanical properties of CLS are analyzed under different loads and load combinations. The results show that: (1) the CLS stress is significantly lower than that of the flat link-slab structure (FLS), (2) its stress values are less than the concrete tensile limit, and (3) the CLS can effectively solve the concrete cracking phenomenon on the link-slab. The rationality of the stress formula derived from the simplified model of the hingeless arch is verified using the finite element method (FEM). The parametric sensitivity analysis shows that variation of the reinforcement ratio of the CLS has a limited impact on it. Considering both the concrete tensile and compressive limit, the thickness of the CLS should be 15 cm to 20 cm, and its design span should be about 5% to7.5% of the main beam length.