Provided is a high-pressure fuel supply pump having a compact and lightweight discharge valve structure and capable of ensuring the oil-sealing performance even at a high fuel pressure. In addition, it is possible to prevent a decrease in the oil-sealing performance due to deformation of a seat part when the valve body of a discharge valve is subject to high back pressure. Furthermore, a flow path is secured while reducing the size and weight. In this high-pressure fuel supply pump a guide part and a curved contact part are provided on the valve body of the discharge valve; therefore, a seat part is formed with Hertzian contact even when high back pressure is applied, and high oil-sealing performance can be achieved. Furthermore, by providing the guide part in the valve body, the curved contact part is limited, and the size and weight of the valve body are reduced.