Variable-deceleration-ratio wide-acceptance-angle electrostatic lens (VD-WAAEL) is proposed as a potential technique for two-dimensional angular and energy analysis. The basic features of the lens are studied using the charge simulation method and ray tracing calculation. The lens uses an ellipsoidal mesh electrode and allows a wide acceptance angle of ±50°. Two possible applications of the VD-WAAEL are discussed. One is a simple combination of the VD-WAAEL-projection-lens, in which an aperture is used for energy analysis. The other is a combination of the VD-WAAEL with a conventional electron spectrometer, which is responsible for obtaining higher energy resolution. The former is discussed in detail and the latter is described briefly. While the ray tracing calculation is only for the case of an ideal mesh, a note on the disturbing effect of mesh holes is presented. The best possible energy resolution of the simple VD-WAAEL-projection-lens analyzer seems to be around 1/1000, given a fine mesh electrode to suppress the disturbing effect of mesh holes.