Abstract: The nonlinear space charge effect of bunched beam in Hnac is one of the important reasons that induces the emittance growth because of the conversion of the field energy to kinetic energy. In this paper, we have worked out the internal field energies associated with some transverse nonuniform space charge distributions of a bunched beam, such as Gaussian distribution, waterbag distribution, and parabolic distribution. And the emittance growth caused by these nonuniformities are obtained.