We report an experimental search for an exotic spin-spin-velocity-dependent interaction between polarized electrons of Rb atoms and polarized electrons of a solid-state mass, violating both the time-reversal and parity symmetries. This search targets a minute effective magnetic field induced by the interaction. A spin-exchange relaxation-free (SERF) magnetometer based on an optically polarized Rb vapor is the key element for both a source of polarized electrons and a high-sensitivity detector. A dysprosium iron garnet (DyIG) serves as the polarized mass, with an extremely small magnetization at the critical temperature around 240 K and a high spin density. To reduce the magnetization, one of major systematic effects, a home-built cooling system controls the mass temperature. To our knowledge, this is the first search for an exotic spin-dependent interaction using the compensated ferrimagnet DyIG as a polarized mass. The experiment set the most stringent limit on the electron-electron coupling strength in the centimeter interaction range, in particular $g_V^e g_V^e <10^{4}$ at $lambda=2$ cm.