Recently, the Bellerophon state, which is a quantized, time dependent, clustering state, was revealed in globally coupled oscillators [Bi et al., Phys. Rev. Lett. 117, 204101 (2016)]. The most important characteristic is that in such a state, the oscillators split into multiple clusters. Within each cluster, the instantaneous frequencies of the oscillators are not the same, but their average frequencies lock to a constant. In this work, we further characterize an intermittent Bellerophon state in the frequency-weighted Kuramoto model with a biased Lorentzian frequency distribution. It is shown that the evolution of oscillators exhibits periodical intermittency, following a synchronous pattern of bursting in a short period and resting in a long period. This result suggests that the Bellerophon state might be generic in Kuramoto-like models regardless of different arrangements of natural frequencies.