The invention relates to an oxycombustion method with capture of the CO2 produced. Mixer M supplies chamber CC with a mixture of oxygen from unit O and of recycled fumes from storage drum SG. Chamber CC is supplied with oxidizer from mixer M and with fuel flowing in through line 8. All of the combustion fumes are sent to water condensation unit CT, then fed into storage drum SG. Part of the fumes containing all the CO2 produced by combustion is compressed to about 60 bars, then cooled and partly liquefied to about 15° C. in liquefaction unit L1, and stored in drum SM. According to the invention, the partly liquefied CO2 is compressed by means of a multiphase pump in order to be discharged through line 16 and stored in an underground reservoir.