Wound tube, which is an important component of coil-wound heat exchanger (CWHE), is subjected to cross-flow impacting and thereby vibrating. Owing to investigating flow-induced vibration (FIV) of wound tubes, it is essential to study the vibration characteristics of the tubes. In this paper, the natural vibration characteristics of wound tube, which was divided into curved tube and coil tube based on support conditions, were studied in detail. And experiments, numerical simulations, and calculation methods were carried out. First, the structures of the two tubes were described parametrically. Afterwards, vibration experiments proved the reliability of numerical simulations of the tubes. Furthermore, calculation methods for the fundamental frequencies of the two tubes were proposed, the accuracies of which were further proven by comparison with simulation results. In addition, the first three mode shapes of the curved tube and coil tube were bending vibration modes. Then the influence of structural parameters on the fundamental frequency was discussed and the independence of parameters was demonstrated. The effects of the variables of the layer pitch ratio, a, the same layer pitch ratio, b, and helix angle, α, on the added mass coefficient, Cm, were ultimately investigated. In general, this paper provides a technical basis to evaluate the design and machining for design and supervision staff.