Direct CP violation in the b-->sgamma process is a sensitive probe of physics beyond the standard model. We report a measurement of the CP asymmetry in B-->X(s)gamma, where the hadronic recoil system X-s is reconstructed using a pseudoreconstruction technique. In this approach there is negligible contamination from b-->dgamma decays, which are expected to have a much larger CP asymmetry. We find A(CP)=0.002+/-0.050(stat)+/-0.030(syst) for B-->X(s)gamma events having recoil mass smaller than 2.1 GeV/c(2). The analysis is based on a data sample of 140 fb(-1) recorded at the Y(4S) resonance with the Belle detector at the KEKB e(+)e(-) storage ring.