ABSTRACT On 2019 April 25, the LIGO/Virgo Scientific Collaboration detected a compact binary coalescence, GW190425. Under the assumption of the binary neutron star (BNS), the total mass of $3.4^{+0.3}_{-0.1}\, \mathrm{M}_⊙$ lies five standard deviations away from the known Galactic population mean. In the standard common envelope scenario, the immediate progenitor of GW190425 is a close binary system composed of an NS and a He-rich star. With the detailed binary evolutionary modelling, we find that in order to reproduce GW190425-like events, super-Eddington accretion (e.g. $1,000\, \dot{M}_{\rm Edd}$) from a He-rich star onto the first-born NS with a typical mass of 1.33 M⊙ via stable Case BB mass transfer (MT) is necessarily required. Furthermore, the immediate progenitors should potentially have an initial mass of MZamsHe in a range of 3.0–3.5 M⊙ and an initial orbital period of Pinit from 0.08 d to 0.12 d, respectively. The corresponding mass accreted onto NSs via stable Case BB MT phase varies from $0.70\, \mathrm{M}_⊙$ to $0.77\, \mathrm{M}_⊙$. After the formation of the second-born NS, the BNSs are expected to be merged due to gravitational wave emission from ∼11 Myr to ∼190 Myr.