We report that an 850-nm vertical-cavity surface-emitting laser with a planar higher order mode absorber, formed by shallow Zn diffusion (<0.3 <mu>m), operated at stable single-mode over the entire drive current range. A device with a 5 x 5 mum(2) absorber aperture and a 5 x 5 mum(2) oxide confined active region showed a similar to0.8 mA threshold and a mode suppression ratio of 40 dB. The modeling indicates that the higher order modes will be suppressed strongly due to the much larger threshold gain, compared to that of the fundamental mode as long as the Zn diffusion depth outside the 5 x 5 mum(2) absorber aperture is over similar to0.2 mum, which agrees well with the experimental results.