The post-merger gravitational wave radiation of the remnant formed in the double neutron star coalescence has not been directly measured, yet. We show in this work that the properties of the binary neutron stars involved in GW170817, additionally constrained by PSR J0030+0451, the lower limit on the maximum gravitational mass of non-rotating neutron star and some nuclear data, are in favor of strong post-merger gravitational wave radiation. This conclusion applies to the mergers of Galactic binary neutron star systems as well. Significant post-merger gravitational wave radiation is also preferred to improve the consistency between the maximum gravitational mass of the non-rotating neutron star inferred from GW170817/GRB170817A/AT2017gfo and the latest mass measurements of pulsars. The prominent post-merger gravitational radiation of GW170817-like events are expected to be detectable by advanced LIGO/Virgo detectors in the next decade and then shed valuable lights on the properties of the matter in the extremely high density.