This paper proposes a novel solid oxide steam electrolyser with in-situ hydrogen storage by integrating a magnesium hydride (MH) section with proton-conducting solid oxide electrolysis cell (SOEC) section. Dynamic simulation results show that it takes 1950 s to fully charge the MH section with a 56% H2 storage efficiency without any flow recirculation, when the electrolyser is operated at 1.4V and 4atm, yielding a current density of 4956.40 A/m2. The evolution of temperature, H2 partial pressure and reaction of Mg powder through the charging process are analysed. It is found that the exothermic H2 absorption process of MH section can enhance the performance of the electrolysis process of SOEC section. The effects of operating parameters including operating pressure, electrolysis voltage, and cooling air temperature on the performance of the novel design are investigated by sensitivity studies. Results show that it is beneficial to operate the electrolyser at elevated pressure for shorter absorption time and higher H2 storage efficiency. Increasing the operating voltage can shorten the absorption time, but lower H2 storage efficiency. An optimal cooling air temperature is found at 521K when the electrolyser is operated at 1.4V and 4atm.