The NOZOMI spacecraft approached the Moon at an altitude of about 2800 km at 0734 UT on December 18, 1998. Around the time of closest approach, a plasma instrument Particle Spectrum Analyzer/Electron Spectrum Analyzer (PSA/ESA) detected non-solar-wind electrons in addition to the normal solar wind component. From the characteristics of the electron distribution function, we can categorize these events into two types: (1) backstreaming electrons exhibiting a velocity distribution similar to that of the solar wind electrons, but its phase space density ratio to the solar wind electrons decreases as a function of velocity; (2) backstreaming electrons that are thermalized and have a flux comparable to or dominating that of the solar wind electrons. We considered possible source locations as well as possible mechanisms that can produce these backstreaming electrons. After careful investigation of the velocity distribution function of the electrons and the magnetic field orientation, we concluded that their origins are (1) the lunar wake region, where the electrostatic potential drop associated with ambipolar plasma expansion reflects the solar wind electrons and produces backstreaming electrons of category 1, and (2) the terrestrial bow shock, where the electrons are thermalized downstream and escaping electrons are of category 2.