The motivation for the present study comes from the appearance of fiber dissolution in industrial applications of composite pipes under different flowing fluids and operating conditions. To mitigate the consequences of glass fiber dissolution in glass fiber reinforced plastics (GRP) pipes, it is essential to investigate the dynamic characteristics of the pipes under internal fluid flow. This paper presents a novel time-dependent micromechanical model and examines the effects of glass fiber dissolution on the instability and vibrational behavior of a composite pipe conveying fluid. The Hamiltonian principle obtains the governing equations of the conveying fluid composite pipe system with fiber dissolution defects. The Finite Element Method (FEM) is then used to solve the eigenvalue problem for the natural frequencies, divergence, and flutter critical velocities of the composite pipe conveying fluid. The effects of different parameters, such as span and amount of dissolution, as well as the quality of the dissolved portion of the fibers, are highlighted on the instability and vibration characteristics of composite pipes. The results show that fiber dissolution significantly affects the behavior of composite pipes conveying fluid. This work also provides a better understanding of the above-mentioned "environmental aging" type in fiber-reinforced composites.