The present invention relates to a process for the partial upgrading of properties of heavy and/or extra-heavy crude oil by low severity catalytic hydrotreatment in only one reaction step. The process of the present invention is obtained upgraded oil with properties required for its transportation from offshore platforms either to maritime terminal or to refining centers. The process reduces the viscosity of heavy and/or extra-heavy crude oil, and decreases the concentration of impurities, such as sulfur, nitrogen, and metals, in such a way that heavy and/or extra-heavy crude oils can be transported to maritime terminals or to refining centers. The process increases the lifetime of the catalyst and decreased operating costs by reducing consumption of utilities because the operation of the process is carried out at lower severity. The partially upgraded oils obtained in this process can be transported directly to the maritime terminals or to existing refineries.