High pressure fuel supply pump for internal combustion engine

The invention relates to a high pressure fuel supply pump having an intake valve (5) automatically opened and closed by pressure of a pressuring chamber (12) being provided in a fuel intake passage (10), the intake valve (5) is pushed to open by a plunger (2) of an electromagnetic plunger mechanism, pulling-in operating timing of the plunger (2) is controlled according to the operating condition of an internal combustion engine, and opening time of the intake valve (5) during compression stroke of a pump is controlled to make discharge flow-rate of high pressure fuel variable.