  Strange stars (SSs) are compact objects made of deconfined quarks. It is hard
to distinguish SSs from neutron stars as a thin crust composed of normal
hadronic matter may exist and obscure the whole surface of the SS. Here we
suggest that the intriguing repeating fast radio bursts (FRBs) are produced by
the intermittent fractional collapses of the crust of an SS induced by
refilling of accretion materials from its low-mass companion. The
periodic/sporadic/clustered temporal behaviors of FRBs could be well understood
in our scenario. Especially, the periodicity is attributed to the modulation of
accretion rate through the disk instabilities. To account for a $\sim 16$-day
periodicity of the repeating FRB source 180916.J0158+65, a Shakura-Sunyaev disk
with a viscosity parameter of $\alpha \simeq 0.004$ and an accretion rate of
$\simeq 3 \times 10^{16}$~g~s$^{-1}$ in the low state is invoked. Our scenario,
if favored by future observations, will serve as indirect evidence for the
strange quark matter hypothesis.
