The intermittent locomotion performance of a fish-like elastic swimmer is studied numerically in this paper. The actuation is imposed only at the head and the locomotion is indirectly driven by passive elastic mechanism. For intermittent swimming, certain time durations of passive coasting are interspersed between two half-periods of active bursting. To facilitate the comparison of energy efficiencies in continuous and intermittent swimming at the same cruising speed, we consider both intermittent swimming at various duty cycles and also continuous swimming at reduced actuation frequencies. The result indicates that the intermittent style is more economical than the continuous style only when the cruising Reynolds number is sufficiently large and the duty cycle is moderate.We also explore the passive tail-beating pattern and wake structure for intermittent swimming. It is found that the kinematics of the tail contains a preparatory burst phase which lies in between the active bursting and the passive coasting phases. Three vortex streets are found in the wake structures behind the intermittent swimmers. The two oblique streets consist of strong vortex dipoles and the horizontal street is made up of weak vortices. The results of this study can provide some insight into the burst-and-coast swimming of fish and also inform the design of efficient bio-mimetic underwater vehicles.