A method for synthesizing methanol, wherein a fuel stream containing carbon is supplied to a synthesis gas reactor arrangement to obtain a synthesis gas stream including hydrogen and carbon oxides that is supplied to a first reactor stage of a methanol reactor arrangement for partial conversion into methanol, and is obtained with a generation pressure higher than the synthesis pressure with which the synthesis gas stream is partially converted into methanol. A residue gas stream is obtained from the methanol reactor arrangement, supplied to a recycle compressor and to the methanol reactor arrangement. Before being supplied to the first reactor stage, the synthesis gas stream is supplied to a heat recovery device to recover heat. A recovery stream is supplied to a hydrogen recovery arrangement to obtain an H-recycle stream. The pressure of the unreacted hydrogen is increased before it is supplied again to the first reactor stage.