We report on zero-field spin splitting of two-dimensional electron systems. Though absent in the unbiased InAs square asymmetric quantum well (SAQW), the Rashba splitting becomes pronounced by applying a positive back-gate voltage. In our SAQW, the Rashba parameter α increases with electron density and is tuned by a factor of about 2 using an additional front gate without charging the well. We argue that the band-edge profile provides the important contribution for spin-orbit interaction due to barrier penetration of the envelope wave function. This mechanism can provide the potential for high speed implementation in spintronics.