  Fast radio bursts (FRBs) are highly dispersed and probably extragalactic
radio flashes with millisecond-duration. Recently, the Canadian Hydrogen
Intensity Mapping Experiment (using the CHIME/FRB instrument) has reported
detections of 13 FRBs during a pre-commissioning phase. It is more exciting
that one of the 13 FRBs is a second source of repeaters which suggests that
CHIME/FRB and other wide-field sensitive radio telescopes will find a
substantial population of repeating FRBs. We have proposed strongly lensed
repeating FRBs as a precision cosmological probe, e.g. constraining the Hubble
constant and model-independently estimating the cosmic curvature. Here, we
study complementary constraints on the equation of state of dark energy from
strongly lensed FRBs to currently available popular probes. It is found that,
in the framework of Chevalier-Polarski-Linder parametrization, adding time
delay measurement of 30 strongly lensed FRB systems to cosmic microwave
background radiation and type Ia supernovae can improve the dark energy figure
of merit by a factor 2. In the precision cosmology era, this improvement is of
great significance for studying the nature of dark energy.
