[en] This paper focuses on studying a Hojman conserved quantity directly derived from a Lie symmetry for a Birkhoffian system in the event space. The Birkhoffian parametric equations for the system are established, and the determining equations of Lie symmetry for the system are obtained. The conditions under which a Lie symmetry of Birkhoffian system in the event space can directly lead up to a Hojman conserved quantity and the form of the Hojman conserved quantity are given. An example is given to illustrate the application of the results