We report here a simple Compton scattering experiment which may be carried out in graduate and undergraduate laboratories to determine the rest mass energy of the electron. In the present experiment, we have measured the energies of the Compton scattered gamma rays with a NaI(Tl) gamma ray spectrometer coupled to a 1 K multichannel analyzer at five scattering angles of [theta] = 30[degrees], 50[degrees], 60[degrees], 70[degrees] and 80[degrees] using a [superscript 137]Cs radioactive gamma source and a suitable aluminum absorber. The rest mass energy of the electron is determined as the reciprocal of the slope of the plot of parameter "S" versus (1 - cos [theta]). The obtained value is found to agree with the standard value. (Contains 2 tables and 8 figures.)