Detection of the gravitational-wave (GW) waveform produced by the coalescence of compact binaries provides a novel way to measure the luminosity distance of the GW events. Combining their redshift information, these sources can be treated as standard sirens to constrain various cosmological parameters. In this article, for various GW detector networks in 2nd-generation (2G), 2.5G and 3G, we comprehensively analyze the method to constrain the equation-of-state (EOS) of binary neutron-stars (BNSs) and extract the redshifts of GW events through the imprints of tidal effects in GW waveforms. We find that, for these GW events, the observations of electromagnetic counterparts (e.g. the kilonovas) in low-redshift range z < 0.1 play a crucial role for constraining the tidal effects. Considering 17 different EOSs of NSs or quark-stars, we find the GW observations have strong capability to determine the EOS, and in 2.5G and 3G era the GW observations can distinguish all the EOS models discussed in this article at high confidence level. Applying the events as standard sirens, and considering the constraints of NS's EOS derived from low-redshift observations as the prior, we can constrain the dark energy, which are quantified by the current dark energy EOS w 0 and its evolution with redshift w a . In the 3G era, the potential constraints are ∆w 0 ∈ (0.0006, 0.004) and ∆w a ∈ (0.004, 0.02), which are 1-3 orders smaller than the potential constraints derived from the traditional electromagnetic methods, including Type Ia supernovas and baryon acoustic oscillations. In particular, in comparison with the widely discussed method of GW standard sirens by fixing the redshifts through short-hard γ-ray bursts, we find the uncertainties of dark energy parameters are reduced by more than one order in magnitude, due to the much more available GW events in this method. Therefore, we conclude that GW standard sirens based on the tidal effect measurement in GW waveform, in combination with the low-redshift observation of electromagnetic counterparts, provide a realizable and much more powerful tool in cosmology.