An operating method in hydrometallurgy of nickel oxide ore comprising a leaching step of adding sulfuric acid to a slurry of nickel oxide ore by using an autoclave, followed by stirring at a temperature of 220 to 280°C to leach the ore under high temperature and pressure conditions, a solid-liquid separation step of separating a leach residue while washing the leach slurry in multi-stages to obtain a leachate containing impurity elements as well as nickel and cobalt, a neutralization step of adding a neutralizing agent to the leachate and separating a neutralized precipitate containing the impurity elements to obtain a neutralization final liquid containing nickel and cobalt, a sulfurization step of subjecting the neutralization final liquid to sulfurization treatment to obtain sulfide containing nickel and cobalt, and barren liquor, an effluent treatment step of adding a neutralizing agent to the barren liquor to adjust its pH to 7.0 to 8.5, so that a neutralized precipitate and an effluent treatment finished solution are solid-liquid separated, a magnesium oxide production step comprising: a calcium separation step of precipitating as calcium sulfate and separating the calcium contained in the effluent treatment finished solution by concentrating the effluent treatment finished solution obtained in the effluent treatment step; a magnesium crystallization step of precipitating as magnesium sulfate and separating the magnesium contained in the solution obtained via the calcium separation step by further concentrating the solution; a roasting step of obtaining magnesium oxide and sulfur dioxide by roasting the magnesium sulfate separated in the magnesium crystallization step together with a reductant; and a washing step of washing the magnesium oxide obtained in the roasting step, wherein the concentration of a solution in the calcium separation step and that in the magnesium crystallization step are performed by natural drying, and wherein the magnesium oxide obtained in the magnesium oxide production step is used as the neutralizing agent that is added in the neutralization step in the hydrometallurgy of the nickel oxide ore. a calcium separation step of precipitating as calcium sulfate and separating the calcium contained in the effluent treatment finished solution by concentrating the effluent treatment finished solution obtained in the effluent treatment step; a magnesium crystallization step of precipitating as magnesium sulfate and separating the magnesium contained in the solution obtained via the calcium separation step by further concentrating the solution; a roasting step of obtaining magnesium oxide and sulfur dioxide by roasting the magnesium sulfate separated in the magnesium crystallization step together with a reductant; and a washing step of washing the magnesium oxide obtained in the roasting step, wherein the concentration of a solution in the calcium separation step and that in the magnesium crystallization step are performed by natural drying, and wherein the magnesium oxide obtained in the magnesium oxide production step is used as the neutralizing agent that is added in the neutralization step in the hydrometallurgy of the nickel oxide ore.