A process for methanol synthesis characterized in that it comprises the following steps: a) providing a syngas feedstream comprising hydrogen and carbon oxides, wherein the carbon oxides are selected from carbon dioxide or a mixture of carbon dioxide and carbon monoxide provided that the molar ratio of carbon dioxide over carbon monoxide in the mixture is equal to or greater than 1.0, and that said syngas feedstream comprises at least 12.0 mol% of CO 2 based on the total molar content of said syngas feedstream; b) providing a first catalytic composition that comprises at least one first methanol synthesis catalyst; c) putting into contact said syngas feedstream with said first catalytic composition under first reaction conditions comprising first temperature conditions, to provide a first gaseous effluent and optionally a first liquid effluent; d) providing a second catalytic composition that comprises at least one second methanol synthesis catalyst wherein said at least one second methanol synthesis catalyst is the same or different from said one first methanol synthesis catalyst; e) putting into contact at least a part of said first gaseous effluent with the second catalytic composition under second reaction conditions comprising second temperature conditions, to provide a second gaseous effluent and a second liquid effluent; f) recovering methanol from one or more selected from the first gaseous effluent and the second gaseous effluent; wherein the first temperature conditions are at least 275°C, wherein the second temperature conditions are lower than the first temperature conditions and second temperature conditions are ranging between 180°C and 250°C, and wherein said first gaseous effluent is subjected to a separation step before being put into contact with the second catalytic composition in step (e) to remove at least a part of methanol and water. a) providing a syngas feedstream comprising hydrogen and carbon oxides, wherein the carbon oxides are selected from carbon dioxide or a mixture of carbon dioxide and carbon monoxide provided that the molar ratio of carbon dioxide over carbon monoxide in the mixture is equal to or greater than 1.0, and that said syngas feedstream comprises at least 12.0 mol% of CO 2 based on the total molar content of said syngas feedstream; b) providing a first catalytic composition that comprises at least one first methanol synthesis catalyst; c) putting into contact said syngas feedstream with said first catalytic composition under first reaction conditions comprising first temperature conditions, to provide a first gaseous effluent and optionally a first liquid effluent; d) providing a second catalytic composition that comprises at least one second methanol synthesis catalyst wherein said at least one second methanol synthesis catalyst is the same or different from said one first methanol synthesis catalyst; e) putting into contact at least a part of said first gaseous effluent with the second catalytic composition under second reaction conditions comprising second temperature conditions, to provide a second gaseous effluent and a second liquid effluent; f) recovering methanol from one or more selected from the first gaseous effluent and the second gaseous effluent; wherein the first temperature conditions are at least 275°C, wherein the second temperature conditions are lower than the first temperature conditions and second temperature conditions are ranging between 180°C and 250°C, and wherein said first gaseous effluent is subjected to a separation step before being put into contact with the second catalytic composition in step (e) to remove at least a part of methanol and water.