This paper deals with a theoretical study of in-plane parametric vibrations of a curved bellows subjected to oscillating internal fluid pressure excitation. In the theoretical analysis, the curved bellows is modeled by FEM (finite element method) using beam elements including the effects of internal fluid mass and dynamic fluid pressure. Mathieu's type equation is derived from the equation of motion of the curved bellows subjected to oscillating internal fluid pressure excitation. Natural frequencies of the curved bellows and parametric instability boundaries are examined theoretically. As a result, two types of parametric vibrations, longitudinal and transverse vibrations, occur to the curved bellows. The longitudinal-parametric instability regions become broader with increasing the axis curvature (curve angle) of the bellows. On the other hand, the transverse-parametric instability regions become narrower.