A 2-D electron energy analyzer is designed and constructed to measure the transverse and longitudinal energy distribution of low energy (<1 eV) electrons. The analyzer operates on the principle of adiabatic invariance and motion of low energy electrons in a strong longitudinal magnetic field. The operation of the analyzer is studied in detail and a design to optimize the energy resolution, signal to noise ratio, and physical size is presented. An energy resolution better than 6 meV has been demonstrated. Such an analyzer is a powerful tool to study the process of photoemission which limits the beam quality in modern accelerators.