Storage of hydrogen is one of the bottlenecks in the hydrogen energy value chain in which liquid storage provides a better solution in terms of higher energy density but suffers from losses during the charging and discharging of tanks. A simulation-based study was performed to investigate coupled heat-transfer, mass-transfer phenomena and pressure rise during the charging and discharging operation of liquid hydrogen fuel in cryogenic storage tank having multilayer insulation under transient conditions. An axis-symmetric two-dimensional analysis was assumed for the tank having overall height 0.518 m and diameter 0.318 m covered by hemispherical top and bottom end with an external steel wall thickness of 3 mm. The thermophysical properties of liquid and vapor are temperature dependent, which were imported from the NIST Chemistry Webbook. In both charging and discharging cases, the inlet condition during the charging process was incorporated using a horizontal radial diffuser and mass-flow outlet during discharging with adiabatic wall conditions. The flow equations were solved using the pressure-implicit splitting of operators (PISO) for pressure–velocity coupling using a commercial Computational Fluid Dynamics (CFD) solver named Ansys Fluent 2021 R1. k-ε turbulence model along with refined mesh near the walls are used to capture the near wall phenomena. The liquid and vapor phase mass transfer occurs through flashing, evaporation, and condensation, which was captured using the Lee model via a user-defined function (UDF). The results are presented regarding pressure rise, temperature distribution along the axis, and vapor and liquid mass variation with time. The charging process starts with flashing to balance the incoming liquid pressure and vapor inside the tank with evaporation around the heated wall and then condensation at a higher filling level followed by compression, causing a higher-pressure rise, limiting the efficiency of the filling process. A change in the initial wall temperature of 50–70 K causes the end pressure to rise from 0.48 MPa up to 0.76 MPa. The discharging process starts with initial condensation due to heat transfer from vapor to liquid. Reduced pressure during discharge reduces the saturation temperature, which causes evaporation or boil-off of liquid hydrogen.