A search for direct CP-violation in K±→π±π0π0 decay based on 47.14 million events has been performed by the NA48/2 experiment at the CERN SPS. The asymmetry in the Dalitz plot linear slopes Ag=(g+−g−)/(g++g−) is measured to be Ag=(1.8±2.6)×10−4. The design of the experiment and the method of analysis provide good control of instrumental charge asymmetries in this measurement. The precision of the result is limited by statistics and is almost one order of magnitude better than that of previous measurements by other experiments.