We report here the first measurements of a diamond-tungsten sampling calorimeter. The calorimeter consisted of twenty layers of diamond with one radiation length of tungsten per layer. The diamond layers were grown by chemical vapor deposition and were 3.0x3.0 cm(2) wafers with an average thickness of 500 mu m. We measured the energy response and resolution (sigma(E)/E) of this calorimeter in 0.5-5.0 GeV electron beams and compared the results with those from a silicon calorimeter of similar construction. Our energy resolution is sigma(E)/E=(4.7+/-2.7)%/E+(19.13+/-0.86)%/root E+(2.3+/-1.8)% for the diamond-tungsten calorimeter, where + indicates addition in quadrature. This is in good agreement with our result for the silicon-tungsten calorimeter of sigma(E)/E=(3.89+/-0.87)%/E+(19.73+/-0.19)%/root E+(0.0+/-1.6)%. We also compare our data with EGS simulations.